CN111625937B - Reliability analysis method for non-probability failure assessment graph - Google Patents
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Abstract
The invention provides a non-probability failure evaluation graph reliability analysis method, which can analyze the reliability of a structure containing defects without accurate failure evaluation points and failure evaluation curves, and provides a reference for the reliability analysis of the structure containing defects. Firstly, based on interval theory and failure evaluation graph theory, a non-probability failure evaluation graph reliability analysis model is established, and failure evaluation points and failure critical points are converted into interval variables. And secondly, combining an interference theory, converting a failure evaluation point and a failure critical point interval into a standardized region, and defining a non-probability failure evaluation graph reliability index eta epsilon [0, + ] according to the relation between the structure limit state function and the standardized region. η=0 represents that the structure is in a failure state, 0 < η < 1 represents the reliability of the structure, and η≡1 represents the safety margin of the structure. Finally, the reliability analysis method of the non-probability failure evaluation graph provided by the invention is verified to be effective by comparing and analyzing with the reliability method of the traditional failure evaluation graph.
Description
Technical Field
The invention belongs to the field of reliability analysis of defect-containing structures, and relates to a reliability analysis method for a non-probability failure evaluation chart.
Background
In engineering practice, actually measured data of the performance of structural materials have dispersibility, the geometric dimension of defects also fluctuates within a tolerance range, the external load of the structure also has uncertainty to a certain extent, and the failure evaluation point and the failure evaluation curve are difficult to accurately determine. The traditional failure evaluation graph theory takes the structural materials and the defect parameters as the determined values, the analysis results only have two conditions, namely the failure and the immediate failure, and under the condition that the failure evaluation points and the failure evaluation curves are difficult to accurately determine, the traditional failure evaluation graph theory can obtain different and even completely opposite analysis results.
In 1999, "European industrial structural integrity assessment method", by 17 organizations in 9 countries, marks a formal establishment of failure assessment graph theory. Currently, failure assessment graph methods are widely accepted by all countries in the world and applied to structural reliability assessment specifications and standards such as European SINTAP[SINTAP,Structural integrity assessment procedures for European industry[S].British Steel,1999.]、 UK R6[R6 Revision 4,Assessment of the integrity of structures containing defects[S].British Energy,2001.]、 UK BS 7910[BS 7910,Guide on Methods for Assessing the Acceptability of Flaws in Metallic Structures[S].British Standards Institute,2013.]、 U.S. API 579[ API 579-1/ASME FFS-1, fitness-For-Service [ S ] American Petroleum Institute,2016 ] and national GB/T19624-2004 [ GB/T19624-2004 ], and have become important methods For analyzing defective structures by industrial departments of all countries in the use of defective stress container safety assessment [ S ]. National standards of the people' S republic of China, 2004 ].
The structural reliability concept based on the male die theory is first proposed in the 90 th century of 20, and the bounded uncertain parameters in the engineering structure are expressed in the form of a non-probabilistic male model. The huge advantage of the non-probability theory to deal with the uncertainty problem is brought into wide attention of the theory world and the engineering world, and an important reference is provided for the reliability analysis of the structure containing the defects.
The invention has the advantage that the reliability of the structure containing the defects can be analyzed without accurate failure evaluation points and failure evaluation curves. When eta=0, the structure is in a failure state, when 0 < eta < 1, the structure is in an incomplete reliable state, eta represents the reliability of the structure, when eta is more than or equal to 1, the structure is in a reliable state, and eta represents the safety margin of the structure. Compared with the traditional reliability analysis method of the failure evaluation graph, the reliability analysis method provided by the invention can effectively solve the reliability analysis problem of the defect-containing structure under the condition that the failure evaluation points and the failure evaluation curve cannot be accurately determined.
Disclosure of Invention
The invention relates to a non-probability failure evaluation chart reliability analysis method, which is used for establishing a non-probability failure evaluation chart reliability analysis model based on interval theory and failure evaluation chart theory. And converting the failure evaluation point and the failure critical point interval into a standardized region, and defining a non-probability failure evaluation graph reliability index according to the relation between the structural limit state function and the standardized region. And combining analysis results of the traditional failure evaluation graph method to verify the effectiveness and feasibility of the method.
The invention mainly comprises the following steps:
step one, establishing a non-probability failure assessment graph reliability analysis model. Based on the interval theory and the failure evaluation graph theory, the failure evaluation points and the failure critical points are converted into interval variable forms.
And step two, the standard area conversion between the failure evaluation point and the failure critical point. Based on interference theory, the failure evaluation point and the failure critical point interval are converted into a standardized region.
And thirdly, defining a reliability index of the non-probability failure evaluation graph. And defining a reliability index of the non-probability failure assessment graph according to the relation between the structure limit state function and the standardized region.
And step four, verifying the reliability analysis method of the non-probability failure evaluation graph. And combining analysis results of the traditional failure evaluation graph method to verify the effectiveness and feasibility of the method.
The method is characterized in that:
(1) And establishing a non-probability failure evaluation graph reliability analysis model based on the interval theory and the failure evaluation graph theory.
(2) Based on interference theory, the failure evaluation point and the failure critical point interval are converted into a standardized region.
(3) And defining a reliability index of the non-probability failure assessment graph according to the relation between the limit state function and the standardized region.
(4) And combining the traditional failure evaluation graph method, and verifying the effectiveness and feasibility of the method.
The invention has the advantages that:
The reliability of the structure containing the defects can be analyzed without the need of accurate failure evaluation points and failure evaluation curves. When eta=0, the structure is in a failure state, when 0 < eta < 1, the structure is in an incomplete reliability state, eta represents the reliability of the structure, when eta is more than or equal to 1, the structure is in a complete reliability state, and eta represents the safety margin of the structure. Compared with the traditional reliability analysis method of the failure evaluation graph, the reliability analysis method provided by the invention can effectively solve the reliability analysis problem of the defect-containing structure under the condition that the failure evaluation points and the failure evaluation curve cannot be accurately determined.
Drawings
FIG. 1 is a non-probabilistic failure assessment graph reliability analysis method framework;
FIG. 2 is a non-probabilistic failure assessment graph reliability analysis model;
FIG. 3 is a normalized zone transition diagram;
Fig. 4M =0 schematically shows the relationship with the normalized area;
FIG. 5 is a schematic diagram of a structural reliability state;
FIG. 6 illustrates parameters;
FIG. 7S (L r,Kr) and R (L rp,Krp) interval variables;
FIG. 8 reliability analysis results;
Detailed Description
The non-probability failure assessment graph reliability analysis method of the invention is further described in detail with reference to the accompanying drawings.
Step one, establishing a non-probability failure assessment graph reliability analysis model. Based on interval theory and failure evaluation graph theory, a non-probability failure evaluation graph reliability analysis model is established, and failure evaluation points and failure critical points are converted into interval variable forms.
Based on interval theory and failure evaluation graph theory, no accurate failure evaluation points and failure evaluation curves are needed, and a non-probability failure evaluation graph reliability analysis model is established, as shown in fig. 2.
F 1(Lr)、f2(Lr) and f 3(Lr) represent inaccurate failure evaluation curves, and according to the structural states when the failure evaluation points fall in different areas of the non-probability failure evaluation graph, the non-probability failure evaluation graph is divided into three areas, namely, a minimum area surrounded by an abscissa L r, an ordinate K r and the failure evaluation curve is defined as a reliable area, areas outside all the failure evaluation curves are defined as failure areas, and areas between the reliable area and the failure areas are defined as uncertain areas. L r andRespectively represent the minimum and maximum values of the failure evaluation point load ratio L r, K r and/>The minimum and maximum values of failure evaluation point fracture ratio K r are shown, respectively. After the ranges of L r and K r are determined, the failure assessment moment can be determined without the distribution form of the failure assessment points. (L r,Kr) (point C)(D point) represents the minimum coordinate point and the maximum coordinate point of the failure evaluation moment, (L rp,Krp) (E point) andAnd (F point) respectively represents a minimum coordinate point and a maximum coordinate point of the intersection of the CD straight line and the failure evaluation curve.
When the load ratio L r and the fracture ratio K r are known, the values of L rp and K rp are obtained
In the same way, can obtainAnd/>Is that
Since L r≥0,Kr≥0,Lrp≥0,Krp is larger than or equal to 0 and the slope of the straight line CD is always larger than zero, it is known that the point on the straight line CD changes monotonically, namely (L r,Kr) and (L rp,Krp) only have two relations.
L r≤Lrp and K r≤Krp (3)
L r＞Lrp and K r＞Krp (4)
In the case of a determined failure assessment moment, the presence of any point (L r,Kr) within the failure assessment moment
Thus, the distance from the failure evaluation point to the origin is herein described asInstead of the coordinate value of the failure evaluation point, only the boundary coordinate value (L r,Kr) and/>, of the failure evaluation point need be determinedThe failure assessment moment can be converted into an interval variable S (L r,Kr).
As can be seen from formula (6), when (L r,Kr) is equal toIn the known case, the median and radius of the S (L r,Kr) interval can be determined without the need for a distribution of failure assessment points
Similarly, the failure critical point can be converted into an interval variable R (L rp,Krp)
As is apparent from the formula (9), at (L r,Kr),In the known case, the median and radius of the R (L rp,Krp) interval can be determined
Then, as shown in the formulas (7) to (11), the failure evaluation points and the failure critical points in the non-probability failure evaluation graph reliability analysis model can be converted into the form of interval variables,
And step two, the standard area conversion between the failure evaluation point and the failure critical point. Based on interference theory, the failure evaluation point and the failure critical point interval are converted into a standardized region.
According to interval theory, R (L rp,Krp) and S (L r,Kr) can be expressed as
R(Lrp,Krp)＝Rc(Lrp,Krp)+Rr(Lrp,Krp)δR (12)
S(Lr,Kr)＝Sc(Lr,Kr)+Sr(Lr,Kr)δS (13)
Wherein, delta R is more than or equal to 0 and delta S is more than or equal to 0 and delta 3935 is more than or equal to 1 and is the standardized variable of R (L rp,Krp) and S (L r,Kr) respectively.
The structure state function can be expressed as
M＝Rr(Lrp,Krp)δR-Sr(Lr,Kr)δS+Rc(Lrp,Krp)-Sc(Lr,Kr) (14)
The critical state function m=0 can be expressed as
Slope of m=0 in normalized region is
Since R (L rp,Krp) and S (L r,Kr) are interval variables, R r(Lrp,Krp) > 0 and S r(Lr,Kr) > 0, there is k > 0.R (L rp,Krp)、S(Lr,Kr) and m=0 can be converted to the normalized region as shown in fig. 3.
And thirdly, defining a reliability index of the non-probability failure evaluation graph. And defining a reliability index of the non-probability failure assessment graph according to the relation between the structure limit state function and the standardized region.
When (when)When M is not less than 0, the structure is in a reliable state, and the reliability index eta of the non-probability failure evaluation chart is defined as
Due toIt is found that η.gtoreq.1, η represents the safety margin of the structure.
When (when)And/>When M may be positive or negative, three cases where m=0 is in the normalized area are shown in fig. 4.
The ratio of the reliable domain area a R to the normalized interval total area a T =4 is defined as the non-probability failure assessment graph reliability index η.
When k > 1, as shown in FIG. 4 (1), the non-probability failure evaluation chart reliability index is
When k=1, as shown in fig. 4 (2), the non-probability failure evaluation chart reliability index is
When 0 < k < 1, as shown in FIG. 4 (3), the reliability index of the non-probability failure evaluation chart is
When (when)Time,/>The structure is in a failure state, and the reliability index of the non-probability failure evaluation graph is defined as eta=0.
Therefore, any state of the structure can be obtained by eta.epsilon.0, +.infinity). When eta is more than or equal to 1, the structure is in a reliable state, and eta represents the safety margin of the structure. When 0 < eta < 1, the structure is in an incompletely reliable state, and eta represents the reliability of the structure. When η=0, the structure is in a failure state.
And step four, verifying the reliability analysis method of the non-probability failure evaluation graph. And combining analysis results of the traditional failure evaluation graph method to verify the effectiveness and feasibility of the method.
According to GB/T19624-2004, taking a failure evaluation curve containing a yield platform and a failure evaluation curve without the yield platform as an example, a non-probability failure evaluation graph model is established.
According to the formulas (21) and (22), a non-probability failure evaluation graph reliability analysis model can be established, and the structure reliability state, the incompletely reliable state and the failure state are respectively shown in fig. 5 (1) - (3).
To fully verify the reliability index of the non-probability failure assessment graph, the reliability, the incompletely reliable state and the failure state are analyzed, K r,L r/>Analysis and verification were performed by taking 10 sets of example parameters from small to large, respectively, as shown in fig. 6.
The S (L r,Kr) and R (L rp,Krp) intervals can be obtained by combining the parameters shown in FIG. 6, as shown in FIG. 7.
The analysis result of the non-probability failure evaluation graph method is respectively compared with the selected different failure evaluation points ((L r,Kr) and (L r,Kr)) The four failure assessment graph method analysis results of the different failure assessment curves (f 1(Lr) and f 2(Lr) are compared as shown in fig. 8.
As shown in examples 1-3 of fig. 8, the analysis results of the non-probabilistic failure assessment graph method are consistent with the analysis results of the most conservative failure assessment graph method, and the structure is in a reliable state.
As shown in examples 4-8 of fig. 8, the reliability analysis results of the structure are different when different failure evaluation points and failure evaluation curves are taken for the conventional failure evaluation graph method. This means that when the failure evaluation point and the failure evaluation curve are taken as fixed values, the failure evaluation point and the failure evaluation curve may result in diametrically opposite analysis results if they are not accurately obtained. The non-probability failure assessment graph method can analyze the structural state of the crack defect in detail and divide the structural state into a reliable state, a non-complete reliable state and a failure state.
As shown in examples 9-10 of fig. 8, the non-probabilistic failure assessment graph method is consistent with the analysis results of the failure assessment graph method under the condition of taking different failure assessment points and failure assessment curves, and the structure is in a failure state.
According to the analysis, the non-probability reliability analysis method provided by the invention can analyze any state of the structure containing the defects. Compared with a method for dividing the structure into failure or reliable binary state failure evaluation graphs, the method for analyzing the reliability of the non-probability failure evaluation graph does not need to analyze the reliability of the structure containing the defects under the condition of accurate failure evaluation points and failure evaluation curves, and subdivides the structure state into three conditions. When eta d is more than or equal to 1, the structure is in a reliable state, when 0 < eta d < 1, the structure is in an incompletely reliable state, and when eta d =0, the structure is in a failure state.
Claims (1)
1. A non-probability failure assessment graph reliability analysis method comprises the following steps:
Step one, establishing a non-probability failure assessment graph reliability analysis model;
Step two, the failure evaluation point is converted with a standardized region of the failure critical point;
step three, defining a reliability index of the non-probability failure evaluation graph;
step four, verifying a reliability analysis method of the non-probability failure evaluation chart;
The method is characterized in that:
step one, establishing a non-probability failure evaluation graph reliability analysis model based on interval theory and failure evaluation graph theory;
with the distance from the failure evaluation point to the origin Instead of the coordinate value of the failure evaluation point, only the boundary coordinate value (L r,Kr) and/>, of the failure evaluation point need be determinedThe failure assessment moment can be converted into an interval variable S (L r,Kr);
L r and Respectively represent the minimum and maximum values of the failure evaluation point load ratio L r, K r and/>Respectively representing the minimum value and the maximum value of failure evaluation point fracture ratio Kr; (L r,Kr) and/>Respectively representing a minimum coordinate point and a maximum coordinate point of the failure evaluation moment;
When (L r,Kr) and In the known case, the median and radius of the S (L r,Kr) interval can be determined without the need for a distribution of failure assessment points
Similarly, the failure critical point can be converted into an interval variable R (L rp,Krp)
(L rp,Krp) andRespectively representing a minimum coordinate point and a maximum coordinate point of the intersection of the straight line and the failure evaluation curve;
At (L r,Kr), In the known case, the median and radius of the R (L rp,Krp) interval can be determined
The failure evaluation points and the failure critical points in the non-probability failure evaluation graph reliability analysis model can be converted into interval variable forms;
step two, converting the failure evaluation point and the failure critical point interval into a standardized region based on an interference theory;
According to interval theory, R (L rp,Krp) and S (L r,Kr) can be expressed as
R(Lrp,Krp)＝Rc(Lrp,Krp)+Rr(Lrp,Krp)δR (12)
S(Lr,Kr)＝Sc(Lr,Kr)+Sr(Lr,Kr)δS (13)
Wherein, delta R is more than or equal to 0 and delta S is more than or equal to 0 and delta 3935 is more than or equal to 1 and is respectively the standardized variables of R (L rp,Krp) and S (L r,Kr);
The structure state function can be expressed as
M＝Rr(Lrp,Krp)δR-Sr(Lr,Kr)δS+Rc(Lrp,Krp)-Sc(Lr,Kr) (14)
The critical state function m=0 can be expressed as
Slope of m=0 in normalized region is
Since R (L rp,Krp) and S (L r,Kr) are interval variables, R r(Lrp,Krp) >0 and S r(Lr,Kr) >0, there is k >0; r (L rp,Krp)、S(Lr,Kr) and m=0 can be converted to the normalized region;
step three, defining a reliability index of the non-probability failure assessment graph according to the relation between the limit state function and the standardized region;
When (when) When M is not less than 0, the structure is in a reliable state, and the reliability index eta of the non-probability failure evaluation chart is defined as
Due toIt can be known that eta is larger than or equal to 1, and represents the safety margin of the structure;
When (when) And/>When the reliability index eta is defined as the ratio of the area A R of the reliable domain to the total area A T =4 of the standardized interval;
when k >1, the non-probability failure assessment graph reliability index is
When k=1, the non-probability failure evaluation graph reliability index is
When 0< k <1, the reliability index of the non-probability failure evaluation chart is that
When (when)Time,/>The structure is in a failure state, and the reliability index of the non-probability failure evaluation graph is defined as eta=0;
Step four, verifying the effectiveness and feasibility of a reliability analysis method of the non-probability failure evaluation graph by combining a traditional failure evaluation graph method;
Establishing a non-probability failure evaluation graph model by using failure evaluation curves containing the yield platform and not containing the yield platform;
Based on the formulas (21) and (22), a non-probability failure evaluation chart reliability analysis model can be established, K r, L r/>And respectively taking 10 groups of parameters from small to large for analysis and verification.
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