Reliability evaluation method for corrugated sandwich structure

Abstract

The invention discloses a corrugated sandwich structure reliability evaluation method, which comprises the following steps of: determining a random variable representing the damage of a corrugated sandwich structure panel, and describing the random variable in an interval form; determining the universe of uncertain variables of the corrugated sandwich structure material, and establishing a double-approximation quantitative model based on limited experimental measurement points according to the uncertain region of the uncertain variables of the material; determining a joint change range of the random variable and the material uncertainty variable, acquiring an initial sample point by adopting Latin hypercube sampling, and calculating a structural response through a finite element model; establishing an initial Kriging model of a random variable, a material uncertainty variable and a structure response, newly adding a sample point based on an expected feasibility function, and updating the Kriging model; and determining a safety threshold of the structure response, and calculating the conservative reliability and aggressive reliability of the corrugated sandwich structure to obtain the overall reliability of the corrugated sandwich structure. The method can improve the reliability of the evaluation structure.

Description

Technical Field

[0001] The invention belongs to the field of mechanical engineering, and in particular relates to a reliability assessment method for a corrugated sandwich structure. Background Art

[0002] Reliability refers to the ability to effectively perform requirements under given conditions and in a given time zone. The reliability problem of a structure is closely linked to the uncertainty problem. As a new type of lightweight multifunctional structure, the corrugated sandwich structure mainly includes upper and lower panels, corrugated webs and filling layers. Due to its excellent mechanical properties and multifunctional design potential, the corrugated sandwich structure is widely used in aviation, aerospace, shipbuilding, machinery and civil engineering. In practical applications, the corrugated sandwich structure may suffer random damage due to manufacturing defects, material aging, external impact and other factors. At the same time, the uncertainty of material parameters further aggravates the nonlinearity of the thermal-mechanical coupling response of the corrugated sandwich structure. Random damage and uncertainty of material parameters will significantly affect the reliability of the structure, especially under dynamic loads or extreme environmental conditions.

[0003] Traditional reliability analysis methods for corrugated sandwich structures are mostly based on deterministic theories. Currently, commonly used reliability analysis models mainly include probabilistic reliability models, non-probabilistic reliability models, and reliability models based on rough set theory. Probabilistic reliability theory has been quite mature, and it has always played an important role in a large number of random phenomena in engineering practice. Under the condition of few samples, the non-probabilistic reliability model is based on convex set theory, uses bounded regions to characterize the uncertainty of uncertain variables, and performs reliability assessment based on measurement methods such as volume ratio. The reliability model based on rough set theory considers the complex correlation between uncertain variables, and uses upper and lower approximate sets to approximate bounded but irregular sets. According to the positional relationship between the response interval boundary and the safety threshold, conservative and radical reliability are defined to evaluate the safety of the structure.

[0004] However, in actual engineering, multiple uncertainties coexist, and a single reliability analysis model has certain limitations. For corrugated sandwich structures, the damage location and degree are random, and a probabilistic reliability model can be used for evaluation. The material parameters of the structure have complex correlations and have small sample characteristics due to measurement cost constraints, so a reliability model based on rough set theory can be used for evaluation. Considering the impact of damage uncertainty and material parameter uncertainty on structural performance at the same time is of great engineering significance for accurately evaluating the failure probability and reliability of corrugated sandwich structures. Therefore, a reliability evaluation method for corrugated sandwich structures that considers multi-source uncertainties and has accurate reliability evaluation is urgently needed. Summary of the invention

[0005] In view of the above problems, an embodiment of the present invention provides a reliability assessment method for a corrugated sandwich structure, which is used to solve the reliability assessment problem of a corrugated sandwich structure under the combined effects of random damage and material parameter uncertainty.

[0006] An embodiment of the present invention provides a method for evaluating the reliability of a corrugated sandwich structure, which includes:

[0007] Step 1: Determine the random variable of damage of the corrugated sandwich structure panel and perform interval description on the random variable;

[0008] Step 2: establishing a domain of material uncertainty variables of the corrugated sandwich structure, and establishing a double approximation quantization model based on finite experimental measurement points according to the uncertainty region of the material uncertainty variables;

[0009] Step 3: According to the interval description and the domain, determine the joint variation range of the material uncertainty variables by Cartesian product operation, obtain initial sample points within the joint variation range by Latin hypercube sampling method, and calculate the structural response corresponding to the sample points by finite element model, wherein the structural response includes temperature response and stress response;

[0010] Step 4: Establishing an initial Kriging model of the random variable, the material uncertainty variable and the structural response, acquiring new sample points based on the expected feasibility function and updating the initial Kriging model to form a corresponding adaptive Kriging model;

[0011] Step 5: using the adaptive Kriging model, calculating the temperature response interval and stress response interval of the corrugated sandwich structure, determining the safety thresholds of the temperature response and the stress response, and calculating the conservative reliability and radical reliability corresponding to the temperature response and the stress response;

[0012] Step 6: Determine the overall conservative and radical reliability of the corrugated sandwich structure based on the serial logical relationship between the structural stress strength failure and the thermal insulation function failure.

[0013] In some possible implementations, determining the damage random variable of the corrugated sandwich structure panel and performing interval description on the random variable includes:

[0014] The panel damage is described by using a rectangular depression, and the random variable is Pos=(x c ,y c ,x r ,y r ,z h ) T , where x c and crepresent the coordinates of the damaged midpoint of the panel along the X-axis and the Y-axis respectively, r and r are the damage lengths of the panel along the X-axis and Y-axis, respectively, h Indicates the damage depth of the panel along the Z-axis direction;

[0015] Each variable in the random variable is characterized in interval form:

[0016]

[0017] The superscripts “L” and “U” represent the lower and upper bounds of the interval, respectively.

[0018] In some possible implementations, an initial Kriging model of the random variable, the material uncertainty variable, and the structural response is established, and additional sample points are acquired based on the expected feasibility function and the initial Kriging model is updated to form a corresponding adaptive Kriging model, including:

[0019] Establishing an initial Kriging model of the random variable, the material uncertainty variable and the temperature response, and an initial Kriging model of the random variable, the material uncertainty variable and the stress response;

[0020] Establish the expected feasibility function (EFF):

[0021]

[0022] where Φ is the cumulative distribution function of the standard normal distribution, φ is the probability density function of the standard normal distribution, σ(s) and are the standard deviation and predicted response value of the initial Kriging model at the input vector s, respectively;

[0023] The optimization algorithm is used to determine the prediction point s corresponding to the maximum expected feasibility function of the initial Kriging model * , and the corresponding response value is calculated by finite element

[0024] The predicted point s * And the corresponding response value The initial Kriging model is reconstructed for the newly added sample points. When the expected feasibility function of the reconstructed Kriging model satisfies max(EFF(s * ))≤0.1% convergence condition, the reconstructed Kriging model forms the adaptive Kriging model.

[0025] In some possible implementations, the corrugated sandwich structure includes a lower panel, a sandwich insulation layer, an upper panel, and a web disposed in the sandwich insulation layer and contacting the upper panel and the lower panel.

[0026] The stress response includes the maximum stress S of the upper panel u , Maximum web stress S w , the temperature response includes the maximum temperature of the lower panel T l , the conservative reliability vector η of the corrugated sandwich structure con and the radical reliability vector η rad They are:

[0027]

[0028] According to the serial logical relationship between structural stress strength failure and thermal insulation function failure, the overall conservative and radical reliability of the corrugated sandwich structure is determined, including:

[0029] When the maximum stress on the upper panel S u , the maximum web stress S w , the maximum temperature of the lower panel T l When any one of the above exceeds the corresponding safety threshold, the corrugated sandwich structure fails, and the overall radical reliability of the corrugated sandwich structure is The overall conservative reliability is

[0030] A method for evaluating the reliability of a corrugated sandwich structure provided by an embodiment of the present invention has at least the following advantages:

[0031] (1) Compared with the traditional reliability analysis model, the embodiment of the present invention simultaneously considers the randomness of the damage of the corrugated sandwich structure and the uncertainty of the material properties, thereby improving the universality of the structural reliability assessment.

[0032] (2) When conducting structural reliability assessment, based on the compatibility of the uniform distribution random quantification model and the interval model, interval variables are used to describe the structural damage, and the double approximation quantification model is used to describe the material uncertainty variables. Based on the boundaries of the temperature and stress response intervals of the structure under the combined action of the two quantification models, conservative and radical reliability indicators are calculated. Further, based on the series relationship between the temperature failure and stress failure of the structure, the reliability of the overall structure is calculated.

[0033] (3) The embodiment of the present invention provides an adaptive Kriging model based on the expected feasibility function learning mechanism, which can quickly solve the limit state function response value, reduce the number of calculations of the finite element model, and improve the calculation efficiency while ensuring the calculation accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 is a flow chart of a reliability assessment method for a corrugated sandwich structure in an embodiment of the present invention;

[0035] Figure 2 A simplified flow chart of a method for evaluating the reliability of a corrugated sandwich structure according to an embodiment of the present invention;

[0036] Figure 3 is a schematic structural diagram of a corrugated sandwich structure in an embodiment of the present invention;

[0037] Figure 4 Schematic diagram of the distribution of aerodynamic thermal load in an embodiment of the present invention.

[0038] Description of reference numerals:

[0039] 10- upper panel;

[0040] 20 - lower panel;

[0041] 30 - abdominal plate;

[0042] 40-Sandwich insulation layer. DETAILED DESCRIPTION

[0043] In order to make the above-mentioned purposes, features and advantages of the embodiments of the present invention more obvious and understandable, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. 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 belong to the scope of protection of the present invention.

[0044] refer to Figure 1 and Figure 2 The embodiment of the present invention provides a method for evaluating the reliability of a corrugated sandwich structure, which specifically includes the following steps:

[0045] Step 1: Determine the random variable of corrugated sandwich structure panel damage and perform interval description of the random variable.

[0046] See also Figure 3 Panel damage is a common damage form of corrugated sandwich structures. In the embodiment of the present application, a set of parameter vectors (i.e., random variables) Pos=(x c ,y c ,x r ,y r ,z h ) T To describe the location and extent of panel damage, where x c and cRespectively represent the damage midpoint ( Figure 3 The coordinates of the X-axis and Y-axis of M are shown in Figure 1, which are the X-axis and Y-axis coordinates of M respectively. r and r are the damage lengths of the panel on the X-axis and Y-axis respectively, such as Figure 3 As shown at B and C, z h Indicates the damage depth of the structure in the Z-axis direction, such as Figure 3 As shown in A in the middle.

[0047] Generally speaking, the location and degree of panel damage are random. Assuming that the probability of panel damage occurring at any location is the same, that is, the five parameters are independent of each other and satisfy the probability density function of uniform distribution. Since the interval model is compatible with the uniform distribution probability model, in this embodiment, we use the interval form to characterize the five random variables:

[0048]

[0049] The superscript "I" represents the interval, and the superscript "L" and superscript "U" represent the lower and upper bounds of the interval, respectively. The variation range U of the damage random variable can be obtained through the Cartesian product:

[0050]

[0051] Step 2: Establish the domain of the material uncertainty variables of the corrugated sandwich structure, and establish a double approximation quantification model based on the uncertainty region of the material uncertainty variables and finite experimental measurement points.

[0052] In the embodiments of this application, see Figure 3 The corrugated sandwich structure includes an upper panel 10, a lower panel 20, a web 30 and a sandwich insulation layer 40, wherein the upper panel 10 is made of Inconel718 material, the web 30 and the lower panel 20 are both made of Ti alloy material, and the sandwich insulation layer 40 is made of Saffil fiber material.

[0053] During the service of the structure, the upper panel 10 is subjected to aerodynamic heat and aerodynamic forces that vary with time, such as Figure 4 As shown, the upper panel 10 is uniformly distributed with aerodynamic heat load, and the lower panel 20 is located inside the wing and conducts natural convection with the air. Considering the processing and measurement errors, the thermal conductivity λ, thermal expansion coefficient α, elastic modulus E of the web 30 are selected. w and the elastic modulus E of the upper panel 10 u As material uncertainty variables. Since the value of material uncertainty variables varies within a certain range, the maximum support set of each material uncertainty variable is described by interval:

[0054]

[0055] Through the Cartesian product operation, the domain V of the material uncertainty variables of the corrugated sandwich structure is obtained:

[0056]

[0057] Thermal conductivity λ, thermal expansion coefficient α and elastic modulus E of the web 30 w The three material uncertainty variables are correlated. The elastic modulus E of the upper panel 10 is u This material uncertainty variable is independent of the above three material uncertainty variables. In actual engineering, the uncertainty variables that characterize the properties of structural materials can be described by bounded irregular regions within the domain, referred to as uncertainty regions. The uncertainty regions of correlated uncertainty variables are called correlated uncertainty regions, and the uncertainty regions of independent material uncertainty variables are called independent uncertainty regions.

[0058] In this embodiment, the Boolean operation of the three-dimensional ellipsoid is used as the uncertainty region of the material uncertainty variable with correlation (ie, the correlation uncertainty region), wherein the region of the ellipsoid Π1 is described as:

[0059]

[0060] The area of ​​the ellipsoid Π2 is described as:

[0061]

[0062] According to Boolean operations, the web thermal conductivity λ, thermal expansion coefficient α and elastic modulus E w The uncertainty area can be described as A1=Π1-Π2.

[0063] The elastic modulus E of the material uncertainty variable with independence w The uncertainty region is A2 = [197,203].

[0064] Finally, the uncertainty region A of the corrugated sandwich structure with respect to the material uncertainty variables is described as the Cartesian product of the dependent uncertainty region A1 and the independent uncertainty region A2, that is, A = A1 × A2.

[0065] A set of measurement points Ψ={ψ1,ψ2,...,ψ m}, where m represents the number of measurement points, represents the i-th measuring point, It represents the web thermal conductivity value, web thermal expansion coefficient value, web elastic modulus value and lower panel elastic modulus value of the i-th experimental measurement point respectively.

[0066] For the thermal conductivity λ of the web 30, each measuring point ψ in the measuring point set Ψi The web thermal conductivity values ​​of (i=1,2,...,m) are sorted and duplicate values ​​are removed, increasing the maximum support set lower bound λ of the thermal conductivity λ L and upper bound λ U , obtain a set of breakpoints from small to large corresponding to the web thermal conductivity λ where r λ Indicates the number of breakpoints corresponding to the thermal conductivity of the web. Similarly, the above method is used to obtain the breakpoint set corresponding to the thermal expansion coefficient of the web, the elastic modulus of the web and the elastic modulus of the lower panel:

[0067]

[0068] According to the above breakpoint set, the maximum support set of each material uncertainty variable can be discretized into the union of multiple subintervals:

[0069]

[0070] Take any subinterval from the multiple subintervals corresponding to each of the above material uncertainty variables, and define the equivalence class of the material uncertainty variable as the union of the multiple subintervals taken:

[0071]

[0072] in Represents the breakpoint set Ψ λ The kth λ breakpoints, Indicates is a discrete subinterval of the left boundary, when k λ =r λ -1, discrete subinterval Convert to a closed subinterval Same reason The breakpoint set Ψ α , The corresponding kth α , breakpoints, and The corresponding sub-intervals are listed in turn.

[0073] For the above equivalence class [x] R For any elements x, y and z in , we assume that they satisfy the equivalence relation R, that is:

[0074]

[0075] In the embodiment of the present application, it is known that the web thermal coefficient λ, thermal expansion coefficient α, elastic modulus E w and the elastic modulus of the lower panel Eu A set of measurement points is shown in Table 1.

[0076] Table 1 Measurement point set of material uncertainty variables

[0077]

[0078] Taking the thermal conductivity of the web as an example, according to the above measurement point set, the corresponding breakpoint set is obtained as follows:

[0079]

[0080] According to the above breakpoint set Ψ λ , the maximum support set λ of the web thermal conductivity λ I It can be discretized into the union of 11 subintervals:

[0081]

[0082] Accordingly, the thermal expansion coefficient α and elastic modulus E of the web can be obtained. w and the elastic modulus of the lower panel E u The breakpoint set of is the subinterval corresponding to the maximum support set. Select one subinterval from each of the multiple subintervals corresponding to each material uncertainty variable to establish the equivalence class of the material uncertainty variable. Taking the first subinterval corresponding to each material uncertainty variable as an example, the established equivalence class is:

[0083]

[0084] In the domain V of four-dimensional material uncertainty variables, there are 14641 equivalence classes. Based on the established equivalence classes and the uncertainty region A of material uncertainty variables, a double approximation quantification model of material uncertainty variables of corrugated sandwich structures is established:

[0085]

[0086]

[0087] in, is the upper approximation set of the uncertain region A, which is composed of the union of equivalence classes in the domain V that are completely or partially contained in the uncertain region A. is the lower approximation set of the uncertain region A, which is composed of the union of equivalence classes in the domain V that are completely contained in the uncertain region A. According to the definition of upper and lower approximation sets, the upper and lower approximation sets and the uncertain region satisfy Therefore, the upper and lower approximation sets are called double approximation quantization models.

[0088] Step 3: According to the interval description and domain, the joint variation range of the material uncertainty variables is determined by the Cartesian product operation, the Latin hypercube sampling method is used to obtain the initial sample points within the joint variation range, and the structural response corresponding to the sample points is calculated by the finite element model. The structural response includes temperature response and stress response.

[0089] In this embodiment, according to the five random variable vectors Pos=(x c ,y c ,x r ,y r ,z h ) T The interval description and the domain V of the material uncertainty variables are used to obtain the joint variation range of all uncertain variables of the corrugated sandwich structure by using the Cartesian product operation:

[0090]

[0091] Within the above joint variation range, 200 sample points are extracted by Latin hypercube sampling to form a sample vector Ξ=(ξ1,ξ2,...,ξ 200 ) T , where ξ i represents the i-th sample point.

[0092] According to the geometric configuration of the corrugated sandwich structure (such as Figure 3 As shown in the figure, a finite element model of the structure is established. The upper panel 10 is subjected to aerodynamic heat flux that changes with time. In addition, since the surface of the structure has a thermal protection coating, the upper panel 10 also has a radiation boundary condition with a radiation coefficient of 0.85. In order to simplify the calculation, the contact thermal resistance of the contact surfaces of different materials and the convection heat transfer and thermal radiation inside the sandwich insulation layer 40 are ignored. At the same time, since the external aerodynamic load of the corrugated sandwich structure is almost zero during service, it is assumed that the air pressure inside the wing is standard atmospheric pressure. At this time, the upper panel 10 is also subjected to an upward static pressure load of 1atm.

[0093] The corrugated sandwich structure is modeled using the temperature-displacement coupling C3D8RT unit, with a total of 57120 units. Based on the birth-death unit method, the panel damage of the corrugated sandwich structure is simulated, and the random variable vector Pos = (x c ,y c ,x r ,y r ,z h ) T The specific value of controls the deletion of the corresponding unit. When the upper surface unit is in the deleted state, the aerodynamic heat load directly acts on the surface of the internal unit. At the same time, the damage of the upper panel 10 means the destruction of the surface coating. The radiation coefficient of the internal unit surface is set to 0.8.

[0094] Stress strength and thermal insulation performance are important contents of the reliability analysis of corrugated sandwich structures. Since the upper panel 10 is made of Inconel718 material, the web 30 and the lower panel 20 are made of Ti alloy material, and the yield strength of different materials is different, the maximum stress S of the upper panel 10 is selected. u , the maximum stress S of the web 30 and the lower panel 20 w As the stress response, the maximum temperature of the lower surface of the corrugated sandwich structure is selected as the temperature response.

[0095] The direct coupling analysis method is used to analyze the thermal-mechanical coupling analysis of the corrugated sandwich finite element model. The maximum stress response vector of the upper panel 10 at 200 sample points is obtained by simulation. The maximum stress response vector of the web 30 and the maximum temperature response vector of the lower surface

[0096] Step 4: Establish an initial Kriging model of random variables, material uncertainty variables and structural responses, obtain new sample points based on the expected feasibility function and update the initial Kriging model to form a corresponding adaptive Kriging model.

[0097] Create a random variable vector Pos = (x c ,y c ,x r ,y r ,z h ) T 、Material uncertainty variable X=(λ,α,E w ,E u ) T , the initial Kriging model of the structural response. The structural response includes the maximum stress response of the upper panel, the maximum stress response of the web, and the maximum temperature response of the lower panel, and three Kriging models are established accordingly.

[0098] The specific process is as follows: random variables and material uncertain variables form uncertain variables, and the 9-dimensional uncertain variable vector s = (x c ,y c ,x r ,y r ,z h ,λ,α,E w ,E u ) is written as the Kriging model form:

[0099]

[0100] Where g(s) is a polynomial function of the uncertain variable vector s, expressed as g(s) = (g1(s), g2(s), ..., g p (s))T ; β is the regression coefficient corresponding to g(s), expressed as β=(β1,β2,...,β p ) T ; z(s) is a variance function with a mean of 0, and its covariance is:

[0101]

[0102] Among them, s i and j are any two uncertain variable vectors, σ represents the standard deviation, is z(s i ) and z(s j ) and the correlation coefficient vector θ. In the embodiment of the present application, the correlation function is a Gaussian correlation function:

[0103]

[0104] in, and Denote the uncertain variable vector s i and j The kth uncertain variable value. According to the sample vector Ξ=(ξ1,ξ2,...,ξ 200 ) T and the corresponding response vector and Three Kriging models are established, the maximum stress response vector in the upper panel below Take this as an example to illustrate.

[0105] Based on the sample vector Ξ=(ξ1,ξ2,...,ξ 200 ) T Establish the regression function matrix of sample points:

[0106]

[0107] The g(s) function uses a linear regression function, and p = 10. At the same time, the correlation coefficient matrix between the 200 sample points is calculated. The element in row i and column j is represents the i-th sample point ξ i With the jth sample point ξ j Calculate the correlation coefficient vector between 200 sample points and the prediction point s The maximum likelihood estimation method is used to solve the unknown parameter θ, and the Kriging model of the maximum stress response of the upper panel is finally obtained as follows:

[0108]

[0109] Similarly, the Kriging model of the maximum stress response of the web and the maximum temperature response of the lower panel can be obtained:

[0110]

[0111] In the embodiment of the present application, the unknown parameters θ of the three Kriging models are:

[0112]

[0113] On the basis of the initial Kriging model, additional sample points are obtained based on the expected feasibility function and the initial Kriging model is updated. Below, the initial Kriging model established based on the maximum stress response of the above panel is explained. First, the following expected feasibility function is established:

[0114]

[0115] where Φ is the cumulative distribution function of the standard normal distribution, φ is the probability density function of the standard normal distribution, σ(s) and are the standard deviation of the input vector s and the predicted response value of the maximum stress on the upper panel, respectively. Taking any input vector s in the 9-dimensional uncertainty space Ω as the independent variable, the Kriging model established above is used to solve the expected feasibility function at s. The following optimization model is established with the maximum as the goal:

[0116]

[0117] sts∈Ω

[0118] The genetic optimization algorithm is used to obtain the maximum point s of the expected feasibility function of the initial Kriging model within the joint variation range Ω of the uncertain variables. * , the corresponding response value S is calculated by finite element u (s * ). Set the expected feasibility function maximum point s * and the corresponding response value S u (s * ) as the new sample point to reconstruct the Kriging model. When the expected feasibility function calculated by the reconstructed Kriging model satisfies When the convergence condition is reached, the last reconstructed Kriging model satisfies the global accuracy of the uncertainty space Ω, forming an adaptive Kriging model. Similarly, the maximum stress response S of the web is established. w The corresponding adaptive Kriging model and the maximum temperature T in the lower panel l The corresponding adaptive kriging model.

[0119] In the embodiment of the present application, based on the expected feasibility function and the convergence condition, the maximum stress response S of the upper panel is uThe corresponding initial Kriging model adds 43 sample points to iterate into the final adaptive Kriging model. The maximum stress response S of the web is w The corresponding initial Kriging model adds 58 sample points to iterate into the final adaptive Kriging model. The maximum stress response T in the lower panel l The corresponding initial Kriging model adds 34 sample points and iterates to become the final adaptive Kriging model.

[0120] Step 5: Use the adaptive Kriging model to calculate the temperature response range and stress response range of the corrugated sandwich structure, determine the safety thresholds of the temperature response and stress response, and calculate the conservative reliability and radical reliability corresponding to the temperature response and stress response.

[0121] Specifically, according to the three adaptive Kriging models established in step 4, and under the interval description of the damage random variable in step 1 and the double approximate quantization model of the material uncertainty variable in step 2, the corresponding upper and lower bounds of the response are calculated:

[0122]

[0123] Where f represents the mapping relationship between the input vector and the corresponding response obtained by the adaptive Kriging proxy model, including the maximum stress mapping relationship on the upper panel Web maximum stress mapping relationship Mapping relationship with the maximum temperature of the lower panel is the corresponding response under the common input of any input variable Pos within the range of damage random variables U and any input vector x in the upper approximate quantization model, It is the corresponding response under the common input of any input variable Pos within the range of damage random variable variation U and any input vector x in the lower approximate quantization model. For the corresponding response The lower bound of the interval, For the corresponding response The upper bound of the interval, For the corresponding response The lower bound of the interval, For the corresponding response The upper bound of the interval.

[0124] Determine safe thresholds for temperature and stress responses in is the safety threshold corresponding to the maximum stress response of the upper panel, is the safety threshold corresponding to the maximum stress response of the web, is the safety threshold corresponding to the maximum temperature response of the lower panel. According to the relationship between any safety threshold δ and the upper and lower bounds of the corresponding response interval, the corresponding radical reliability η is calculated.rad and conservative reliability η con for:

[0125]

[0126] in, Finally, the radical reliability corresponding to the maximum stress response of the upper panel can be obtained and conservative reliability Radical reliability corresponding to the maximum stress response of the web and conservative reliability Aggressive reliability corresponding to the maximum temperature response of the lower panel and conservative reliability

[0127] Exemplarily, according to the three adaptive Kriging models established in step 4, under the interval description of the damage random variable in step 1 and the double approximation quantization model of the material uncertainty variable in step 2, the response intervals of the three responses are calculated as follows:

[0128]

[0129] The yield strength of the Inconel718 material used in the upper panel 10 is 800MPa, the yield strength of the titanium alloy material of the web is 980MPa, and the maximum temperature of the lower panel exceeds 600K, which is considered to be a functional failure of the structure. Therefore, the safety thresholds of the three responses of the structure are determined as follows: and According to the safety threshold and the above response range, the radical reliability and conservative reliability of different responses are calculated as follows:

[0130]

[0131] Step 6: Determine the overall conservative and radical reliability of the corrugated sandwich structure based on the serial logical relationship between structural stress strength failure and thermal insulation function failure.

[0132] When the maximum stress at different parts of the corrugated sandwich structure exceeds the yield limit of the material used in that part, it is considered that the overall structure has stress strength failure. At the same time, the corrugated sandwich structure has thermal insulation performance. Once the maximum temperature of the lower surface of the structure exceeds the given temperature safety threshold, the thermal insulation function of the structure is considered to have failed. When any failure form occurs in the structure, the corrugated sandwich structure can be considered to have failed as a whole, that is, the multiple failure forms satisfy a series logical relationship.

[0133] According to the above series logic relationship and the radical and conservative reliability under different responses calculated in step 5, the overall radical reliability of the corrugated sandwich structure is obtained. and overall radical reliability for:

[0134]

[0135] For example, according to the radical and conservative reliability of the three responses calculated in step 5, the overall radical reliability of the corrugated sandwich structure is finally obtained: and overall radical reliability for:

[0136]

[0137] In the embodiments of the present application, the randomness of the damage of the corrugated sandwich structure panel and the uncertainty of the material properties are considered at the same time. Compared with the traditional reliability analysis model that only considers the uncertainty of the material, the reliability evaluation result is more universal. In addition, the bounded irregular area is approximately characterized based on the limited experimental measurement points and the double approximation quantization model, breaking through the limitation of the rule quantization of the traditional convex model method. At the same time, the series relationship between the temperature failure and stress failure of the corrugated sandwich structure is taken into account to calculate the overall reliability of the structure, making the final evaluation result more practical. The adaptive Kriging model based on the expected feasibility function is used to quickly solve the limit state function response value, which can reduce the number of calculations of the finite element model and effectively improve the calculation efficiency while ensuring the global accuracy of the calculation.

[0138] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "illustrative embodiments", "examples", "specific examples", or "some examples" means that the specific features, structures, materials, or characteristics described in conjunction with the embodiments or examples are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described may be combined in any one or more embodiments or examples in a suitable manner.

[0139] 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 replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for evaluating the reliability of a corrugated sandwich structure, characterized in that: include: Step 1: Determine the random variable of damage of the corrugated sandwich structure panel and perform interval description on the random variable; Step 2: establishing a domain of material uncertainty variables of the corrugated sandwich structure, and establishing a double approximation quantization model based on finite experimental measurement points according to the uncertainty region of the material uncertainty variables; Step 3: According to the interval description and the domain, determine the joint variation range of the material uncertainty variables by Cartesian product operation, obtain initial sample points within the joint variation range by Latin hypercube sampling method, and calculate the structural response corresponding to the sample points by finite element model, wherein the structural response includes temperature response and stress response; Step 4: Establishing an initial Kriging model of the random variable, the material uncertainty variable and the structural response, acquiring new sample points based on the expected feasibility function and updating the initial Kriging model to form a corresponding adaptive Kriging model; Step 5: using the adaptive Kriging model, calculating the temperature response interval and stress response interval of the corrugated sandwich structure, determining the safety thresholds of the temperature response and the stress response, and calculating the conservative reliability and radical reliability corresponding to the temperature response and the stress response; Step 6: Determine the overall conservative and radical reliability of the corrugated sandwich structure based on the serial logical relationship between the structural stress strength failure and the thermal insulation function failure.

2. The reliability assessment method of the corrugated sandwich structure according to claim 1, characterized in that: Determine the damage random variable of the corrugated sandwich structure panel, and perform interval description on the random variable, including: The panel damage is described by using a rectangular depression, and the random variable is Pos=(x c ,y c ,x r ,y r ,z h ) T , where x c and c represent the coordinates of the damaged midpoint of the panel along the X-axis and the Y-axis respectively, r and r are the damage lengths of the panel along the X-axis and Y-axis, respectively, h Indicates the damage depth of the panel along the Z-axis direction; Each variable in the random variable is characterized in interval form: The superscripts "L" and "U" represent the lower and upper bounds of the interval, respectively.

3. The reliability assessment method of the corrugated sandwich structure according to claim 1, characterized in that: Establishing an initial Kriging model of the random variable, the material uncertainty variable and the structural response, acquiring new sample points based on the expected feasibility function and updating the initial Kriging model to form a corresponding adaptive Kriging model, including: Establishing an initial Kriging model of the random variable, the material uncertainty variable and the temperature response, and an initial Kriging model of the random variable, the material uncertainty variable and the stress response; Establish the expected feasibility function (EFF): where Φ is the cumulative distribution function of the standard normal distribution, φ is the probability density function of the standard normal distribution, σ(s) and are the standard deviation and predicted response value of the initial Kriging model at the input vector s, respectively; The optimization algorithm is used to determine the prediction point s corresponding to the maximum expected feasibility function of the initial Kriging model * , and the corresponding response value is calculated by finite element The predicted point s * And the corresponding response value The initial Kriging model is reconstructed for the newly added sample points. When the expected feasibility function of the reconstructed Kriging model satisfies max(EFF(s * ))≤0.1% convergence condition, the reconstructed Kriging model forms the adaptive Kriging model.

4. The reliability assessment method of a corrugated sandwich structure according to claim 1, characterized in that: The corrugated sandwich structure comprises a lower panel, a sandwich insulation layer, an upper panel which are stacked in sequence, and a web which is arranged in the sandwich insulation layer and contacts the upper panel and the lower panel; The stress response includes the maximum stress S of the upper panel u , Maximum web stress S w , the temperature response includes the maximum temperature of the lower panel T l , the conservative reliability vector η of the corrugated sandwich structure con and the radical reliability vector η rad They are: According to the serial logical relationship between structural stress strength failure and thermal insulation function failure, the overall conservative and radical reliability of the corrugated sandwich structure is determined, including: When the maximum stress on the upper panel S u , the maximum web stress S w , the maximum temperature of the lower panel T l When any one of the above exceeds the corresponding safety threshold, the corrugated sandwich structure fails, and the overall radical reliability of the corrugated sandwich structure is The overall conservative reliability is

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