CN113901612A - Structural member degradation modeling and reliability pre-estimating method and system - Google Patents

Structural member degradation modeling and reliability pre-estimating method and system Download PDF

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CN113901612A
CN113901612A CN202111191259.5A CN202111191259A CN113901612A CN 113901612 A CN113901612 A CN 113901612A CN 202111191259 A CN202111191259 A CN 202111191259A CN 113901612 A CN113901612 A CN 113901612A
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郭宇
张海军
薛璐
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Jiangsu XCMG Construction Machinery Institute Co Ltd
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Abstract

The invention discloses a method and a system for structural member degradation modeling and reliability estimation. The method comprises the following steps: establishing a fatigue accumulated damage model under a stable working condition; describing the occurrence frequency of the impact working condition through a Poisson process, describing the duration of the impact working condition by a normal model, expressing the acceleration effect of non-Gaussian load generated by the impact working condition on structural damage by a correction factor method, and establishing a fatigue accumulated damage model under the impact working condition; accumulating the fatigue accumulated damage model under the stable working condition and the fatigue accumulated damage model under the impact working condition to obtain a damage degradation model; and calculating to obtain a distribution function of the accumulated degradation amount of the structural member according to a full probability formula based on the damage degradation model, and evaluating the reliability of the structural member according to the distribution function. The method has the advantages of unified calculation model, simple calculation method and improvement of the estimation accuracy of the fatigue reliability of the structural member.

Description

Structural member degradation modeling and reliability pre-estimating method and system
Technical Field
The invention belongs to the technical field of reliability estimation, and particularly relates to a structural member degradation modeling and reliability estimation method and system considering impact load effect.
Background
When the engineering machinery is used, the structural parts of the engineering machinery bear various dynamic loads, and fatigue damage can be generated under the action of alternating loads, so that the structure is cracked, product failure is caused, and even potential safety accidents are caused. The working load of the engineering machinery has stable working conditions such as hoisting, flat ground and the like, and also has impact working conditions such as crushing, piling and the like. The fatigue damage speed of the structural member can be greatly accelerated under the impact working condition, so that the method has important theoretical significance and application value for accurately describing the load characteristic under the impact working condition, establishing a corresponding degradation model and estimating the reliability of the structural member.
The main technical scheme for predicting the fatigue reliability of the metal structural part comprises the following steps: (1) a fatigue reliability estimation method based on a time domain, and (2) a fatigue reliability estimation method based on a frequency domain. For the first, the time domain damage is calculated by counting a segment of random time domain signals, long signal acquisition is required in the time domain to accurately describe random response, and the time domain signals are difficult to process. Stress amplitude and mean distribution are generally obtained by a rain flow counting method, damage calculation and inference are carried out, cyclic counting is needed, and data processing capacity is large. The method needs to acquire the working profile load in advance, the existing method only generally analyzes and processes the typical stable working condition load and does not take the impact working condition load into account, so that the estimation accuracy of the reliability of the structural member is low. For the second kind, because the frequency of the impact working condition load is higher than that of the steady working condition load, the method is beneficial to considering the influence of the high-frequency load type on the reliability, but in the engineering problem, the fatigue failure mechanism of all the working condition load types is considered to be consistent, namely, the damage rule of the impact working condition load is processed according to the steady working condition load, the acceleration effect of the impact working condition load on the fatigue is not reflected, so that the fatigue reliability estimation result is biased to be falsely estimated.
Disclosure of Invention
The invention aims to provide a method and a system for estimating degradation modeling and reliability of a structural member under the condition of simultaneously considering a stable working condition and an impact working condition load so as to accurately estimate the reliability of the structural member.
In order to achieve the purpose, the invention adopts the following technical scheme:
on one hand, the method for structural component degradation modeling and reliability estimation comprises the following steps:
taking the load of the structural member in the stable working condition process as a Gaussian load, and establishing a fatigue accumulated damage model under the stable working condition by adopting a wiener process;
the method comprises the steps of considering the load of a structural member in the process of an impact working condition as an ultra-high Gaussian load, describing the occurrence frequency of the impact working condition through a Poisson process, describing the duration time of the impact working condition by a normal model, describing the acceleration effect of the ultra-Gaussian load on the structural member in the impact working condition by a correction factor method, and establishing a fatigue accumulated damage model under the impact working condition by adopting a wiener process;
accumulating the fatigue accumulated damage model under the stable working condition and the fatigue accumulated damage model under the impact working condition to obtain a damage degradation model under the combined action of the stable working condition and the impact working condition;
based on the damage degradation model, calculating to obtain a distribution function of the accumulated degradation quantity of the structural part according to a full probability formula;
and evaluating the reliability of the structural member according to the distribution function of the accumulated degradation quantity of the structural member.
Further, regarding the load of the stable working condition process of the structural member as a gaussian load, establishing a fatigue accumulated damage model under the stable working condition by adopting a wiener process, specifically comprising:
obtaining an S-N curve of a structural part:
NSb＝A (1)
in the formula: s is a stress amplitude, N is the cycle number of fatigue failure, and b and A are fatigue characteristic parameters of the structural member metal material;
a frequency domain method is adopted to represent the operation process under the stable working condition:
ni＝υptdp(Si)dSi (2)
in the formula: n isiNumber of stress cycles for i-th order stress level, tdIn order to stabilize the fatigue action time in the working process under the working condition,Siis the i-th order stress amplitude, p (S)i) Is a probability density function of the i-th stress amplitude, upsilonpThe peak rate.
The fatigue damage formula is:
Figure BDA0003301285030000031
in the formula: k is the cyclic stress level; n is a radical ofiTo a stress amplitude of SiThe fatigue life cycle times of the structural member; d is a fatigue accumulated damage value;
according to the formula (1), the formula (2) and the formula (4), the fatigue accumulated damage value of the structural part under the stable working condition is calculated as follows:
Figure BDA0003301285030000032
in the formula:
Figure BDA0003301285030000033
represents the damage in unit time, and t is the service life of the structural part;
the utilization rate of the structural member is set as a random variable eta ∈ [0,1 ] and has randomness according to the utilization rate of the structural member]Assuming that the mean value is muηVariance is ση 2And then converting the fatigue accumulated damage value under the stable working condition into:
D(η,t)＝ηBt
describing the fatigue accumulated damage value by adopting a wiener process to obtain a fatigue accumulated damage model under a stable working condition:
D(t)～N(μt,σ2t)
in the formula: mu-muηB, the drift parameter is; sigma2＝B2ση 2The diffusion coefficient is shown.
Further, the S-N curve is obtained through a fatigue test or a related standard according to the material and the state of the metal material for the structural member.
Further, the description of the occurrence frequency of the impact condition through the poisson process includes:
considering the impact working condition process as a poisson random process with the strength of lambda, the probability that the impact occurs for i times when the service life time t of the structural member is reached is as follows:
Figure BDA0003301285030000041
in the formula: n (t) is the number of times of impact occurrence when the service life time t of the structural part is reached;
according to the basic properties of the poisson process, the average value E (n (t)) λ t of the number of times of impact occurrence and the variance Var (n (t)) λ t of the number of times of impact occurrence at the structural member life time t are obtained.
Further, the describing the duration of the impact condition by the normal model includes:
according to the moment t when the structural part is impacted1,t2,…tiIs random and has a corresponding action time t of each impact processs1,ts2,…tsiAssuming that the impact time of the impact condition is normally distributed:
Figure BDA0003301285030000042
in the formula, TsA random variable representing the impact time of each impact process, and the value of the random variable can be ts1,ts2,…tsi。
Further, the impact time TsThe distribution of (a) is obtained by analyzing sample data obtained by the test.
Further, the super-Gaussian load generated by the impact condition introduces the following correction factors into the acceleration effect of the damage to the structural member:
ω＝1+α(k-3)
in the formula: ω is a correction factor, k is the kurtosis of the stress response, α is a positive proportionality coefficient, and when k is 3, the correction factor ω is 1; when the kurtosis k of the stress response is >3, the correction factor ω > 1.
Further, the fatigue accumulated damage model under the impact condition is established by the following method:
a frequency domain method is adopted to represent the operation process of a certain impact working condition:
ni＝υ′ptsp′(Si)dSi (3)
in the formula: n isiNumber of stress cycles for level i impact stress, tsFor a certain impact time, SiIs the i-th order impact stress amplitude, p' (S)i) Is a probability density function of the impact stress amplitude of the ith stage, upsilon'pIs the peak impact rate;
the formula of fatigue damage caused by a certain impact is represented by formula (4);
according to the formula (1), the formula (3) and the formula (4), introducing a correction factor of the ultra-high Gaussian distribution fatigue generated under the impact working condition, and calculating to obtain an accumulated damage value caused by the impact action when the structural member reaches the service life time t, wherein the accumulated damage value is as follows:
Figure BDA0003301285030000051
in the formula:
Figure BDA0003301285030000052
TN(t)is the sum of random impact time, and omega is a correction factor of the ultrahigh Gaussian distribution fatigue generated under the impact working condition;
mean cumulative damage from impact
Figure BDA0003301285030000061
Variance of
Figure BDA0003301285030000062
From the mean and variance of the sum of random variables:
Figure BDA0003301285030000063
Figure BDA0003301285030000064
in the formula: e (T)N(t)) Is the mean of the sum of random impact times, Var (T)N(t)) Variance of sum of random impact times, E (T)s) As the time of impact TsMean value of, Var (T)s) As the time of impact TsThe variance of (a) is determined,
therefore, μs(t)＝ωB′λμst，σs(t) 2＝(ωB′)2λ(σs 2+μs 2)t；
According to the randomness of accumulated damage in the impact process, describing an accumulated damage value caused by the impact action by adopting a wiener process to obtain a fatigue accumulated damage model under the impact working condition:
S(t)～N(μ't,σ'2t)
in the formula: mu '═ ω B' λ μs，σ'2＝(ωB′)2λ(σs 2+μs 2)。
Further, the damage degradation model is:
M(t)＝D(t)+S(t)～N((μ+μ′)t,(σ2+σ′2)t)
in the formula: m (t) is the accumulated degradation amount of the structural part under the combined action of the steady working condition and the impact working condition.
Further, the distribution function of the accumulated degradation amount of the structural member is as follows:
Figure BDA0003301285030000065
in the formula: x is the degradation magnitude, and P (m) (t) > x, n (t) ═ i) is the failure probability distribution function of the degradation magnitude of the structure.
Further, the reliability of the structural member is:
Figure BDA0003301285030000071
in the formula: r (t) is the reliability of the structural member, tau is the fatigue damage threshold value, and tau is less than or equal to 1.
In another aspect, a system for structural degradation modeling and reliability prediction includes:
the first model building module is configured to regard the load of the structural part in the stable working condition process as a Gaussian load, and build a fatigue accumulated damage model under the stable working condition by adopting a wiener process;
the second model building module is configured to regard the load of the structural member in the process of the impact working condition as the ultrahigh Gaussian load, describe the occurrence frequency of the impact working condition through a Poisson process, describe the duration time of the impact working condition by a normal model, describe the acceleration effect of the ultrahigh Gaussian load generated by the impact working condition on the damage of the structural member by a correction factor method, and build a fatigue accumulated damage model under the impact working condition by a wiener process;
the third model building module is configured to accumulate the fatigue accumulated damage model under the stable working condition and the fatigue accumulated damage model under the impact working condition to obtain a damage degradation model under the combined action of the stable working condition and the impact working condition;
the calculation module is configured to calculate and obtain a distribution function of the accumulated degradation quantity of the structural member according to a total probability formula based on the damage degradation model;
and the reliability evaluation module is configured to evaluate the reliability of the structural member according to the distribution function of the accumulated degradation amount of the structural member.
Compared with the prior art, the invention has the following beneficial technical effects:
(1) the influence of impact working conditions on the accumulated damage of the structural member is considered, and the estimation accuracy of the fatigue reliability of the structural member is improved;
(2) the same degradation modeling method is adopted for the stable working condition and the single impact process, the acceleration effect of the single non-Gaussian impact load is expressed by using a correction factor method, the calculation models are unified, and the calculation method is simple.
Drawings
FIG. 1 is a flow chart of a method for modeling degradation of a structural member and estimating reliability of the structural member in consideration of an impact load effect according to an embodiment of the present invention;
FIG. 2 is a graph of the fatigue total damage degradation trajectory;
FIG. 3 is a graph of reliability for a structure taking into account only the steady load and both the steady and impact loads;
FIG. 4 is a block diagram of a structural member degradation modeling and reliability prediction system in accordance with an embodiment of the present invention.
Detailed Description
The invention is further described with reference to specific examples. The following examples are only for illustrating the technical solutions of the present invention more clearly, and the protection scope of the present invention is not limited thereby.
In one embodiment, as shown in fig. 1, a method for structural component degradation modeling and reliability prediction includes:
step S11, regarding the load of the structural member in the stable working condition process as a Gaussian load, and establishing a fatigue accumulated damage model under the stable working condition by adopting a wiener process;
according to the material and the state of the metal material for the structural part, an S-N curve is obtained through a fatigue test or a related standard, namely:
NSb＝A (1)
in the formula: s is the stress amplitude, N is the cycle number of fatigue failure, and b and A are the fatigue characteristic parameters of the structural member metal material.
According to the operation mode of the engineering machinery, the operation working condition is divided into a stable working condition represented by hoisting and flat ground operation and an impact working condition represented by crushing and piling operation, and the load courses of the stable working condition and the impact working condition are respectively analyzed through tests or simulation.
The load under the stable working condition is continuously distributed, and is expressed by a frequency domain method as follows:
ni＝υptdp(Si)dSi (2)
in the formula: n isiNumber of stress cycles for i-th order stress level，tdWorking process fatigue action time for steady working condition, SiIs the i-th order stress amplitude, p (S)i) Is a probability density function of the i-th stress amplitude, upsilonpThe peak rate, i.e., the average number of peaks occurring per unit time of the random stress sequence.
The fatigue damage formula under the stable working condition is as follows:
Figure BDA0003301285030000091
in the formula: k is the cyclic stress level; n is a radical ofiTo a stress amplitude of SiThe fatigue life cycle times of the structural member; d is a fatigue accumulated damage value;
the fatigue accumulated damage value (i.e. the degradation amount) of the structural member under the stable working condition is calculated by the formulas (1), (2) and (4):
Figure BDA0003301285030000092
in the formula:
Figure BDA0003301285030000093
it can be understood as damage per unit time and t is the structural member life.
Because the utilization rate of the structural member has randomness, the utilization rate is set as a random variable eta which belongs to [0,1 ]]The mean and variance can be obtained through the actual data statistics of the structural part, and the mean is assumed to be muηVariance is ση 2And then converting the fatigue accumulated damage value under the stable working condition into:
D(η,t)＝ηBt (6)
considering the randomness of accumulated damage in the stable process, describing the fatigue accumulated damage value by adopting a wiener process to obtain a fatigue accumulated damage model under the stable working condition:
D(t)～N(μt,σ2t) (7)
in the formula: mu-muηB, the drift parameter is; sigma2＝B2ση 2The diffusion coefficient is shown.
Step S12, regarding the load in the structural member impact working condition process as an ultra-high Gaussian load, describing the occurrence frequency of the impact working condition through a Poisson process, describing the duration time of the impact working condition by a normal model, describing the acceleration effect of the ultra-Gaussian load generated by the impact working condition on the structural member by a correction factor method, and establishing a fatigue accumulation damage model under the impact working condition by adopting a wiener process;
the impact condition load is also distributed continuously, and a certain impact condition operation process can be expressed as follows:
ni＝υ′ptsp′(Si)dSi (3)
in the formula: n isiNumber of stress cycles for level i impact stress, tsFor a certain impact time, SiIs the i-th order impact stress amplitude, p' (S)i) Is a probability density function of the impact stress amplitude of the ith stage, upsilon'pIs the peak impact rate;
the formula of fatigue damage caused by a certain impact can be expressed by the formula (4).
Considering the impact working condition operation process as a poisson random process with the strength of lambda, the probability that the impact occurs for i times when the service life time t of the structural member is reached is as follows:
Figure BDA0003301285030000101
in the formula: n (t) is the number of impact occurrences at time t when the structural member has reached its life.
According to the basic properties of the poisson process, the average value E (n (t)) λ t of the number of times of impact occurrence and the variance Var (n (t)) λ t of the number of times of impact occurrence at the structural member life time t are obtained.
Moment t when the structural part is impacted1,t2,…tiIs random, ts1,ts2,…tsiIs the action time of each impact process and is independent of each other. Impact time T of impact conditionsIs a random variable, which is divided intoThe cloth is usually obtained by analyzing sample data obtained experimentally, and it can be assumed as a normal distribution, that is:
Figure BDA0003301285030000111
in the formula, TsA random variable representing the time of each impact, which may be ts1,ts2,…tsi。
The impact working condition load accords with the super Gaussian distribution, and a correction factor of the super Gaussian distribution fatigue is introduced:
ω＝1+α(k-3) (10)
in the formula: ω is a correction factor, k is the kurtosis of the stress response, α is a positive proportionality coefficient, and when the kurtosis k of the stress response is 3, i.e. the response is gaussian distribution, ω is 1; when the kurtosis k of the stress response is greater than 3, i.e. the response stress is in a super gaussian distribution, the correction factor ω is greater than 1, which indicates that the super gaussian distribution accelerates the fatigue accumulation damage of the structure, and the more pronounced the super gaussian characteristic is, the more pronounced this acceleration effect is.
According to the formulas (1), (3) and (4), introducing a correction factor of super-Gaussian distribution fatigue, and calculating to obtain an accumulated damage value (namely, a degradation amount) caused by the impact action of the structural member at the time t reaching the service life as follows:
Figure BDA0003301285030000112
in the formula:
Figure BDA0003301285030000121
TN(t)is the sum of random impact times.
Mean cumulative damage from impact
Figure BDA0003301285030000122
Variance of
Figure BDA0003301285030000123
From the mean and variance of the sum of random variables:
Figure BDA0003301285030000124
Figure BDA0003301285030000125
wherein, E (T)N(t)) Is the mean of the sum of random impact times, Var (T)N(t)) Variance of sum of random impact times, E (T)s) As the time of impact TsMean value of, Var (T)s) As the time of impact TsThe variance of (a) is determined,
therefore, μs(t)＝ωB′λμst，σs(t) 2＝(ωB′)2λ(σs 2+μs 2)t。
Considering the randomness of accumulated damage in the impact process, describing by adopting a wiener process to obtain a fatigue accumulated damage model under the impact working condition:
S(t)～N(μ't,σ'2t) (14)
in the formula: mu '═ ω B' λ μs，σ'2＝(ωB′)2λ(σs 2+μs 2)。
Step S13, accumulating the fatigue accumulated damage model under the stable working condition and the fatigue accumulated damage model under the impact working condition to obtain a damage degradation model under the combined action of the stable working condition and the impact working condition;
regardless of the correlation between the degradation of the stationary process and the degradation of the impact process, the total degradation of the structural member should be composed of the degradation d (t) of the stationary operation process and the degradation s (t) of the impact operation process, which can be expressed as:
M(t)＝D(t)+S(t)～N((μ+μ′)t,(σ2+σ′2)t) (15)
in the formula: m (t) is the accumulated degradation amount of the structural part under the combined action of the steady working condition and the impact working condition.
Step S14, based on the damage degradation model, according to a total probability formula, calculating to obtain a distribution function of the accumulated degradation quantity of the structural member as follows:
Figure BDA0003301285030000131
in the formula: x is the degradation value, and P (m) (t) > x, n (t) ═ i) is the failure probability distribution function of the degradation value of the structure.
And step S15, evaluating the reliability of the structural member according to the distribution function of the accumulated degradation quantity of the structural member.
Wherein the reliability function of the structural member is:
Figure BDA0003301285030000132
in the formula: r (t) is the reliability of the structural member, tau is a fatigue damage threshold value, tau is less than or equal to 1, and tau takes a value of 0.9 in the application. The fatigue total damage amount degradation trajectory is shown in fig. 2.
The reliability of a structural member predicted only by considering the steady load working condition and the reliability of the structural member predicted by the method of the embodiment of the invention simultaneously considering the steady load and the impact load working condition are compared through the following specific embodiments:
under a stable working condition, the fatigue damage threshold tau is assumed to be 0.9, and the accumulated damage obeys the wiener process D (t) to N (0.00058t, 0.0042)2t), then the reliability of structure is:
Figure BDA0003301285030000141
considering the influence of the impact load on the structural member, the impact load reaches the strength of lambda being 0.0005, and the accumulated damage of the smooth load is subjected to the wiener process d (t) to N (0.00058t, 0.0042)2t) cumulative damage of impact load obeys wiener process S (t) to N (0.0014t, 0.0086)2t) structureThe total degradation amount of the piece is M (t) to N (0.00198t, 0.00957)2t), the reliability of the structural member is as follows under the condition that the fatigue damage threshold value tau of the structural member is 0.9:
Figure BDA0003301285030000142
the change curve of the reliability of the structural member along with time under the working conditions of stable load, stable load and impact load are respectively considered as shown in fig. 4, and specific values are shown in the following table 1.
TABLE 1
Figure BDA0003301285030000143
As can be seen from fig. 4 and table 1, the reliability of the structural member predicted by the method of the embodiment of the present invention, which considers both the steady load and the impact load, is more suitable for the actual situation and more accurate than the reliability of the structural member predicted by considering only the steady load.
Through the embodiment, the degradation modeling and reliability estimating method for the structural part, provided by the invention, describes the degradation rule of the structural part under a stable working condition through an accumulated damage process; describing the occurrence frequency of the impact working condition through a Poisson process, describing the duration of the impact working condition by a normal model, and expressing the acceleration effect of the non-Gaussian load generated by the impact working condition on the structural damage by a correction factor method; and establishing a damage degradation model under the combined action of a stable working condition and an impact working condition, and further accurately estimating the reliability of the structural member.
In another embodiment, a structural component degradation modeling and reliability prediction system comprises:
the first model building module is configured to regard the load of the structural part in the stable working condition process as a Gaussian load, and build a fatigue accumulated damage model under the stable working condition by adopting a wiener process;
the second model building module is configured to regard the load of the structural member in the process of the impact working condition as the ultrahigh Gaussian load, describe the occurrence frequency of the impact working condition through a Poisson process, describe the duration time of the impact working condition by a normal model, describe the acceleration effect of the ultrahigh Gaussian load generated by the impact working condition on the damage of the structural member by a correction factor method, and build a fatigue accumulated damage model under the impact working condition by a wiener process;
the third model building module is configured to accumulate the fatigue accumulated damage model under the stable working condition and the fatigue accumulated damage model under the impact working condition to obtain a damage degradation model under the combined action of the stable working condition and the impact working condition;
the calculation module is configured to calculate and obtain a distribution function of the accumulated degradation quantity of the structural member according to a total probability formula based on the damage degradation model;
and the reliability evaluation module is configured to evaluate the reliability of the structural member according to the distribution function of the accumulated degradation amount of the structural member.
The present invention has been disclosed in terms of the preferred embodiment, but is not intended to be limited to the embodiment, and all technical solutions obtained by substituting or converting equivalents thereof fall within the scope of the present invention.

Claims (12)

1. A structural component degradation modeling and reliability pre-estimation method is characterized by comprising the following steps:
taking the load of the structural member in the stable working condition process as a Gaussian load, and establishing a fatigue accumulated damage model under the stable working condition by adopting a wiener process;
the method comprises the steps of considering the load of a structural member in the process of an impact working condition as an ultra-high Gaussian load, describing the occurrence frequency of the impact working condition through a Poisson process, describing the duration time of the impact working condition by a normal model, describing the acceleration effect of the ultra-Gaussian load on the structural member in the impact working condition by a correction factor method, and establishing a fatigue accumulated damage model under the impact working condition by adopting a wiener process;
accumulating the fatigue accumulated damage model under the stable working condition and the fatigue accumulated damage model under the impact working condition to obtain a damage degradation model under the combined action of the stable working condition and the impact working condition;
based on the damage degradation model, calculating to obtain a distribution function of the accumulated degradation quantity of the structural part according to a full probability formula;
and evaluating the reliability of the structural member according to the distribution function of the accumulated degradation quantity of the structural member.
2. The structural member degradation modeling and reliability estimating method according to claim 1, wherein the load of the structural member in the stable working condition process is regarded as a gaussian load, and a fatigue accumulated damage model under the stable working condition is established by adopting a wiener process, specifically comprising:
obtaining an S-N curve of a structural part:
NSb＝A (1)
in the formula: s is a stress amplitude, N is the cycle number of fatigue failure, and b and A are fatigue characteristic parameters of the structural member metal material;
a frequency domain method is adopted to represent the operation process under the stable working condition:
ni＝υptdp(Si)dSi (2)
in the formula: n isiNumber of stress cycles for i-th order stress level, tdWorking process fatigue action time for steady working condition, SiIs the i-th order stress amplitude, p (S)i) Is a probability density function of the i-th stress amplitude, upsilonpThe peak rate.
The fatigue damage formula is:
Figure FDA0003301285020000021
in the formula: k is the cyclic stress level; n is a radical ofiTo a stress amplitude of SiThe fatigue life cycle times of the structural member; d is a fatigue accumulated damage value;
according to the formulas (1), (2) and (4), the fatigue accumulated damage value of the structural part under the stable working condition is calculated as follows:
Figure FDA0003301285020000022
in the formula:
Figure FDA0003301285020000023
represents the damage in unit time, and t is the service life of the structural part;
the utilization rate of the structural member is set as a random variable eta ∈ [0,1 ] and has randomness according to the utilization rate of the structural member]Assuming that the mean value is muηVariance is ση 2And then converting the fatigue accumulated damage value under the stable working condition into:
D(η,t)＝ηBt
describing the fatigue accumulated damage value by adopting a wiener process to obtain a fatigue accumulated damage model under a stable working condition:
D(t)～N(μt,σ2t)
in the formula: mu-muηB, the drift parameter is; sigma2＝B2ση 2The diffusion coefficient is shown.
3. The structural member degradation modeling and reliability prediction method according to claim 2, wherein the S-N curve is obtained through fatigue tests or related standards according to the material and state of the metal material for the structural member.
4. The structural member degradation modeling and reliability prediction method according to claim 2, wherein describing the occurrence frequency of the impact condition through a poisson process comprises:
considering the impact working condition process as a poisson random process with the strength of lambda, the probability that the impact occurs for i times when the service life time t of the structural member is reached is as follows:
Figure FDA0003301285020000031
in the formula: n (t) is the number of times of impact occurrence when the service life time t of the structural part is reached;
according to the basic properties of the poisson process, the average value E (n (t)) λ t of the number of times of impact occurrence and the variance Var (n (t)) λ t of the number of times of impact occurrence at the structural member life time t are obtained.
5. The structural member degradation modeling and reliability prediction method according to claim 4, wherein describing the duration of the impact condition with a normal model comprises:
according to the moment t when the structural part is impacted1,t2,…tiIs random and has a corresponding action time t of each impact processs1,ts2,…tsiAssuming that the impact time of the impact condition is normally distributed:
Figure FDA0003301285020000032
in the formula, TsA random variable representing the impact time of each impact process, and the value of the random variable can be ts1,ts2,…tsi。
6. A structural member degradation modeling and reliability prediction method as claimed in claim 5 wherein the impact time T issThe distribution of (a) is obtained by analyzing sample data obtained by the test.
7. The structural member degradation modeling and reliability prediction method according to claim 1, wherein the super-Gaussian load generated by the impact condition introduces the following correction factors to the acceleration effect of the damage of the structural member:
ω＝1+α(k-3)
in the formula: ω is a correction factor, k is the kurtosis of the stress response, α is a positive proportionality coefficient, and when k is 3, the correction factor ω is 1; when the kurtosis k of the stress response is >3, the correction factor ω > 1.
8. A structural member degradation modeling and reliability prediction method according to claim 5, wherein the fatigue accumulated damage model under the impact condition is established by the following method:
a frequency domain method is adopted to represent the operation process of a certain impact working condition:
ni＝υ′ptsp′(Si)dSi (3)
in the formula: n isiNumber of stress cycles for level i impact stress, tsFor a certain impact time, SiIs the i-th order impact stress amplitude, p' (S)i) Is a probability density function of the impact stress amplitude of the ith stage, upsilon'pIs the peak impact rate;
the formula of fatigue damage caused by a certain impact is represented by formula (4);
according to the formulas (1), (3) and (4), introducing a correction factor of the ultrahigh-Gaussian distribution fatigue generated under the impact working condition, and calculating to obtain an accumulated damage value caused by the impact action when the structural member reaches the service life time t, wherein the accumulated damage value is as follows:
Figure FDA0003301285020000041
in the formula:
Figure FDA0003301285020000042
TN(t)is the sum of random impact time, and omega is a correction factor of the ultrahigh Gaussian distribution fatigue generated under the impact working condition;
mean cumulative damage from impact
Figure FDA0003301285020000051
Variance of
Figure FDA0003301285020000052
From the mean and variance of the sum of random variables:
Figure FDA0003301285020000053
Figure FDA0003301285020000054
in the formula: e (T)N(t)) Is the mean of the sum of random impact times, Var (T)N(t)) Variance of sum of random impact times, E (T)s) As the time of impact TsMean value of, Var (T)s) As the time of impact TsThe variance of (a) is determined,
therefore, μs(t)＝ωB′λμst，σs(t) 2＝(ωB′)2λ(σs 2+μs 2)t；
According to the randomness of accumulated damage in the impact process, describing an accumulated damage value caused by the impact action by adopting a wiener process to obtain a fatigue accumulated damage model under the impact working condition:
S(t)～N(μ't,σ'2t)
in the formula: mu '═ ω B' λ μs，σ'2＝(ωB′)2λ(σs 2+μs 2)。
9. The structural member degradation modeling and reliability prediction method according to claim 8, wherein the damage degradation model is:
M(t)＝D(t)+S(t)～N((μ+μ′)t,(σ2+σ′2)t)
in the formula: m (t) is the accumulated degradation amount of the structural part under the combined action of the steady working condition and the impact working condition.
10. The method of claim 9, wherein the distribution function of the cumulative degradation of the structure is:
Figure FDA0003301285020000061
in the formula: x is the degradation magnitude, and P (m) (t) > x, n (t) ═ i) is the failure probability distribution function of the degradation magnitude of the structure.
11. The method of claim 10, wherein the reliability of the structural component is as follows:
Figure FDA0003301285020000062
in the formula: r (t) is the reliability of the structural member, tau is the fatigue damage threshold value, and tau is less than or equal to 1.
12. A structural member degradation modeling and reliability prediction system is characterized by comprising:
the first model building module is configured to regard the load of the structural part in the stable working condition process as a Gaussian load, and build a fatigue accumulated damage model under the stable working condition by adopting a wiener process;
the second model building module is configured to regard the load of the structural member in the process of the impact working condition as the ultrahigh Gaussian load, describe the occurrence frequency of the impact working condition through a Poisson process, describe the duration time of the impact working condition by a normal model, describe the acceleration effect of the ultrahigh Gaussian load generated by the impact working condition on the damage of the structural member by a correction factor method, and build a fatigue accumulated damage model under the impact working condition by a wiener process;
the third model building module is configured to accumulate the fatigue accumulated damage model under the stable working condition and the fatigue accumulated damage model under the impact working condition to obtain a damage degradation model under the combined action of the stable working condition and the impact working condition;
the calculation module is configured to calculate and obtain a distribution function of the accumulated degradation quantity of the structural member according to a total probability formula based on the damage degradation model;
and the reliability evaluation module is configured to evaluate the reliability of the structural member according to the distribution function of the accumulated degradation amount of the structural member.
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