Reliability analysis method for complex structure equipment under measurement condition

Abstract

The invention provides a reliability analysis method for complex structure equipment under the condition of considering measurement, and belongs to the field of reliability analysis. According to the reliability analysis method, firstly, a finite element model of the complex structure equipment is established, and structural response is obtained; secondly, measuring points are arranged on the considered complex structure; then, constructing an accurate conditional probability density function expression of the reliability index when the measurement condition is considered; and solving a conditional probability density function of the reliability index when the measurement condition is considered by using a generalized quasi Monte Carlo method. And finally, completing reliability analysis of the structure based on a conditional probability density function. According to the method, the conditional probability density function containing the mechanical probability index under the measurement condition is deduced and solved based on the probability conservation law in combination with the generalized quasi Monte Carlo method, reliability analysis of complex structure equipment is completed, the precision is high, the calculation efficiency is good, and a more reliable basis is provided for structural safety and reliability analysis.

Description

Technical Field

[0001] The invention belongs to the field of reliability analysis and relates to a reliability analysis method for complex structure equipment under measurement conditions. Background Art

[0002] Structural reliability estimation plays a vital role in the engineering field, especially in the design of buildings, aerospace, bridges, machinery and other structures that need to withstand physical stress. Structural reliability not only involves the safety of the structure, but also includes applicability and durability. It is quantitatively analyzed through a probabilistic indicator - structural reliability. In the process of design, construction and use, due to various uncertainties, the evaluation of structural reliability becomes complicated and necessary.

[0003] The commonly used structural reliability calculation methods include Monte Carlo method, surrogate model method, first-order second moment method, etc. The Chinese invention patent "A method for time-varying reliability analysis of bearings considering the coupling effect of rolling contact fatigue damage and wear" (patent number: 202411171631.X) proposes a novel physical model for bearing reliability analysis, establishes the RCF damage and wear coupling effect of the bearing, and more reasonably and accurately evaluates the reliability while significantly improving the calculation efficiency. The Chinese invention patent "Surrogate model method for reliability analysis of turbine casing under evidence uncertainty" (patent number: 202311359650.0) can robustly and quickly calculate the failure probability limit of the turbine casing structure under evidence uncertainty, thereby reasonably evaluating the reliability level of the turbine casing. However, these inventions all study the reliability analysis method of structures without measurement conditions. In many engineering problems, such as building health monitoring, engineers usually arrange measurement points on the structure to measure the structural response. This reliability analysis method of structures with measurement conditions has not yet been studied. When using random parameters to quantify the random dynamic response of a structure, if the measurement data conditions can be considered, it is obvious that the uncertainty quantification of the random response can be further refined, providing a more reliable basis for structural safety and reliability analysis. At the same time, in actual engineering problems, the measurement errors caused by human operation and instrument errors are also random.

[0004] Therefore, how to accurately and effectively evaluate the reliability of complex structural equipment under measurement conditions with random errors is an extremely important issue. Summary of the invention

[0005] In view of the problems existing in the prior art, the present invention provides a reliability analysis method for complex structural equipment under measurement conditions. Based on the law of conservation of probability, the present invention derives an accurate expression of the conditional probability density function containing the mechanical probability index under measurement conditions. Compared with the analysis under unconditional conditions, the reliability analysis method for complex structural equipment under measurement conditions proposed by the present invention can produce more accurate results, thereby providing a more solid basis for the safety and reliability assessment of the structure. The present invention fills the gap in the research on reliability analysis of structural equipment when measurement data exists.

[0006] In order to achieve the above object, the technical solution adopted by the present invention is:

[0007] A reliability analysis method for complex structural equipment under measurement conditions. The reliability analysis method first establishes a finite element model of the complex structural equipment to obtain the structural response. Secondly, the measuring points are arranged on the complex structure under consideration. Then, an accurate conditional probability density function expression of the reliability index when the measurement conditions are considered is constructed. The generalized quasi-Monte Carlo method is then used to solve the conditional probability density function of the reliability index when the measurement conditions are considered. Finally, the reliability analysis of the structure is completed based on the conditional probability density function. The following steps are included:

[0008] The first step is to establish a finite element model of complex structural equipment to obtain the structural response; specifically:

[0009] Step 1.1, import an existing complex structure equipment model into the 3D modeling software, or model the 3D model of the complex structure equipment according to the engineering drawing to obtain a finite element model of the complex structure equipment.

[0010] Step 1.2, based on the finite element model of the complex structure equipment established in step 1.1, determine the corresponding material properties, constraints and loads of the complex structure equipment according to the actual problem.

[0011] Step 1.3: Determine the uncertain random variables in complex structural equipment according to actual needs , and the probability density function of the variable When there are multiple uncertain variables, is a vector, each component of which corresponds to a different uncertainty variable.

[0012] Based on the above steps, the finite element model of complex structural equipment, load constraints and the distribution of uncertainty variables are obtained. When the value is , it can be substituted into the finite element model of complex structure equipment to calculate the complex structure equipment Time response .

[0013] The second step is to arrange the measuring points on the complex structure equipment under consideration, specifically:

[0014] Step 2.1: Arrange measurement points at key nodes of complex structural equipment, conduct measurements, and obtain actual measurement values. , the measurements are accumulated over time. The key node locations can be determined based on experience or historical data.

[0015] Step 2.2: Random measurement errors are inevitable in the measurement process. Determine the test noise based on the range of the selected measuring instrument. Set the measurement noise as a stationary Gaussian process. It means that its probability density is .

[0016] Step 2.3, known measured value and measurement noise Then, the measurement equation is obtained:

[0017] (1)

[0018] in, It is the measurement function of complex structural equipment, which describes the measurement value and structural response under the condition of no measurement noise. the relationship between; express Simplified writing of ; Indicates the time value.

[0019] The third step is to construct the precise conditional probability density function expression of the reliability index considering the measurement conditions, specifically:

[0020] Step 3.1: Define the mechanical reliability indicators to be analyzed , the mechanical reliability index Yes Response is a function of, and therefore an uncertain random variable Therefore, Expressed as .

[0021] Step 3.2, solve the known measurement data conditions hour, The conditional probability density function of , It is expressed as:

[0022] (2)

[0023] in, for The joint probability density of The measured value The probability density of .

[0024] According to the law of conservation of probability, the joint probability density of the system consisting of the finite element model of complex structural equipment and the measurement conditions is Written as:

[0025] (3)

[0026] in, is the Dirac function, the function value is zero at all points except the zero point, and the integral over the entire domain is equal to 1; represents the joint probability density function of the measurement noise at all time steps, The definition of is as detailed in step 1.3. This means that when the measurement noise at all time steps is exactly When , the corresponding value of the joint probability density function;

[0027] pass For random variables and measurement noise The integral of the marginal probability density is , as shown in formula (4):

[0028] (4)

[0029] Again Points:

[0030] (5)

[0031] At this time, and Substitute as the numerator and denominator into the probability density function expression (2) to obtain the known measurement data condition hour, The conditional probability density function of .

[0032] The fourth step is to use the generalized quasi-Monte Carlo method to calculate the conditional probability density function of the reliability index when considering the measurement conditions. Specifically:

[0033] Step 4.1: Use the quasi-Monte Carlo method to solve This is a high-dimensional integral.

[0034] First, a generalized low-bias sampling method is used to quantify the random variables in the complex structure equipment under consideration. Sampling is carried out. Sampling follows The probability distribution of Sample points , and find the corresponding point set weight .

[0035] Will obtain Sample points Substitute it into the finite element model of the complex structure equipment in step 1.1 and calculate the corresponding Then, the measured value is calculated using the generalized quasi-Monte Carlo calculation format shown in formula (6) The probability density function of :

[0036] (6)

[0037] Step 4.2, is a high-dimensional integral containing a non-smooth Dirac function and cannot be calculated directly. It is necessary to first use a Gaussian function to approximate the Dirac function and then use the generalized quasi-Monte Carlo method to solve it. At this time, formula (4) is rewritten as:

[0038] (7)

[0039] Among them, when using Gaussian function approximation, Represents the smoothing factor.

[0040] Step 4.3, the obtained and Substituting into formula (2), The solution is complete.

[0041] The fifth step is to complete the reliability analysis of complex structure equipment based on the conditional probability density function, as follows:

[0042] Step 5.1: Determine the normal use of the complex structure equipment under consideration according to the actual problem. The allowed threshold .

[0043] Step 5.2, the reliability probability of complex structure equipment is expressed as ,use , and numerically integrate and solve it to obtain the reliability probability of complex structure equipment, and complete the reliability analysis of complex structure equipment.

[0044] Compared with the prior art, the present invention has the following beneficial effects:

[0045] (1) Based on the law of conservation of probability and combined with the generalized quasi-Monte Carlo method, the present invention derives and solves the conditional probability density function of the mechanical probability index under measurement conditions, completes the reliability analysis of complex structural equipment, and solves the reliability problem of complex structural equipment when measurement conditions exist for the first time, filling the gap in the research on reliability analysis of structural equipment when measurement data exists.

[0046] (2) Compared with the unconditional case, the reliability analysis method of complex structural equipment under the condition of measurement provided by the present invention obtains more accurate results, providing a more reliable basis for structural safety and reliability analysis.

[0047] (3) The present invention adopts the generalized quasi-Monte Carlo method to calculate high-dimensional integral problems. Compared with the traditional Monte Carlo method and the quasi-Monte Carlo method, it requires fewer sample points, has higher accuracy and better calculation efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 It is a flow chart of the reliability analysis method for complex structural equipment under measurement conditions.

[0049] Figure 2 Schematic diagram of the finite element model of the bridge and the locations of the measuring points in the embodiment. DETAILED DESCRIPTION

[0050] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, completes the reliability analysis of a bridge, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0051] A reliability analysis method for complex structural equipment under measurement conditions is provided. In this embodiment, the complex structural equipment is a bridge, and the reliability analysis method includes the following steps:

[0052] The first step is to establish a finite element model of the bridge, specifically:

[0053] Step 1.1, import the existing bridge model into the 3D modeling software to obtain the bridge finite element model.

[0054] Step 1.2, based on the bridge finite element model established in step 1.1, the material of the bridge frame is structural steel, and the elastic modulus is , the shear modulus is , the density is The bridge deck thickness is 0.5m, the Poisson's ratio is 0.5, and the bridge deck material is concrete with a density of

[0055] Step 1.3: Determine the uncertain random variables in the bridge according to actual needs , and the probability density function of the variable For this embodiment, is a 10-dimensional column vector, each component of which corresponds to a different uncertainty variable.

[0056] Based on the above steps, the finite element model of the bridge, the load constraints and the distribution of uncertainty variables are obtained. When the value is , it can be substituted into the bridge finite element model to calculate the bridge point A and point B at Time response .

[0057] The second step is to arrange the measuring points on the bridge under consideration, specifically:

[0058] Step 2.1: Arrange measuring points at the key nodes of the bridge. The measuring points are located as follows: Figure 2 The midpoints C1, C2, and C3 are shown, and the actual measured values ​​are obtained. ,The measurements are accumulated over time. The locations of key nodes are determined based on ,empirical judgment.

[0059] Step 2.2: Random measurement errors are inevitable in the measurement process. Determine the test noise based on the range of the selected measuring instrument. Set the measurement noise as a stationary Gaussian process. It means that its probability density is ,in represents the covariance matrix of the measurement noise, Indicates the number of iteration time steps.

[0060] Step 2.3, known measured value and measurement noise Then, the measurement equation is obtained:

[0061] (1)

[0062] in, is the measurement function of the bridge, which describes the relationship between the measured values ​​and the structural response without measurement noise. the relationship between; express Simplified writing of ; Indicates the time value.

[0063] The third step is to construct the precise conditional probability density function expression of the reliability index considering the measurement conditions, specifically:

[0064] Step 3.1: Define the mechanical reliability indicators to be analyzed , the mechanical reliability index Yes Response is a function of, and therefore an uncertain random variable Therefore, Expressed as .

[0065] Step 3.2, solve the known measurement data conditions hour, The conditional probability density function of , It is expressed as:

[0066] (2)

[0067] in, for The joint probability density of The measured value The probability density of .

[0068] According to the law of conservation of probability, the joint probability density of the system consisting of the bridge finite element model and the measurement conditions is Written as:

[0069] (3)

[0070] in, It is a Dirac function, which has a value of zero at all points except the zero point, and its integral over the entire domain is equal to 1. represents the joint probability density function of the measurement noise at all time steps, The definition of is as detailed in step 1.3. This means that when the measurement noise at all time steps is exactly When , the corresponding value of the joint probability density function;

[0071] pass For random variables and measurement noise The integral of the marginal probability density is , as shown in formula (4):

[0072] (4)

[0073] Again Points:

[0074] (5)

[0075] At this time, and Substitute as the numerator and denominator into the probability density function expression (2) to obtain the known measurement data condition hour, The conditional probability density function of .

[0076] The fourth step is to use the generalized quasi-Monte Carlo method to calculate the conditional probability density function of the reliability index when considering the measurement conditions. Specifically:

[0077] Step 4.1: Use the quasi-Monte Carlo method to solve This is a high-dimensional integral.

[0078] First, a generalized low-bias sampling method is used to sample the random variables in the bridge under consideration. Sampling is carried out. Sampling follows The probability distribution of Sample points , and find the corresponding point set weight .

[0079] Will obtain Sample points Substitute it into the bridge finite element model in step 1.1 and calculate the corresponding Then, the measured value is calculated using the generalized quasi-Monte Carlo calculation format shown in formula (6) The probability density function of :

[0080] (6)

[0081] Step 4.2, is a high-dimensional integral containing a non-smooth Dirac function and cannot be calculated directly. It is necessary to first use a Gaussian function to approximate the Dirac function and then use the generalized quasi-Monte Carlo method to solve it. At this time, formula (4) is rewritten as:

[0082] (7)

[0083] Among them, when using Gaussian function approximation, Represents the smoothing factor.

[0084] Step 4.3, the obtained and Substituting into formula (2), The solution is complete.

[0085] The fifth step is to complete the reliability analysis of the bridge based on the conditional probability density function, as follows:

[0086] Step 5.1: Determine the normal use of the bridge under consideration according to the actual problem. The allowed threshold .

[0087] Step 5.2, the reliability probability of the bridge is expressed as ,use , perform numerical integration to solve it and obtain the reliability probability of the bridge, thus completing the reliability analysis of the bridge.

[0088] The above-described embodiments merely express the implementation methods of the present invention, but they cannot be understood as limiting the scope of the patent of the present invention. It should be pointed out that for those skilled in the art, several modifications and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention.

Claims

1. A reliability analysis method for complex structure equipment under measurement conditions, characterized in that: The reliability analysis method comprises the following steps: The first step is to establish a finite element model of complex structural equipment and obtain the structural response; The second step is to arrange the measuring points on the complex structure equipment under consideration and obtain the measurement equation; The third step is to construct the exact conditional probability density function expression of the reliability index considering the measurement conditions; The fourth step is to use the generalized quasi-Monte Carlo method to calculate the conditional probability density function of the reliability index when considering the measurement conditions; The fifth step is to complete the reliability analysis of complex structural equipment based on the conditional probability density function.

2. A reliability analysis method for complex structure equipment under measurement conditions according to claim 1, characterized in that: The first step comprises the following steps: Step 1.1, importing an existing complex structure equipment model into a 3D modeling software, or modeling the 3D model of the complex structure equipment according to an engineering drawing, to obtain a finite element model of the complex structure equipment; Step 1.2, based on the finite element model of the complex structure equipment established in step 1.1, determine the corresponding material properties, constraints and loads of the complex structure equipment according to the actual problem; Step 1.3: Determine the uncertain random variables in complex structural equipment according to actual needs , and the probability density function of the variable ; When there are multiple uncertain variables, is a vector, each component of which corresponds to a different uncertainty variable; Based on the above steps, the finite element model of complex structural equipment, the distribution of load constraints and uncertainty variables are obtained; when given When the value is substituted into the finite element model of complex structure equipment, the complex structure equipment is calculated Time response .

3. The reliability analysis method for complex structure equipment under measurement conditions according to claim 1 is characterized in that: The second step comprises the following steps: Step 2.1: Arrange measurement points at key nodes of complex structural equipment, conduct measurements, and obtain actual measurement values. , measurements are accumulated over time; Step 2.2: During the measurement process, determine the test noise according to the range of the measuring instrument; set the measurement noise as a stationary Gaussian process, using It means that its probability density is ; Step 2.3, known measured value and measurement noise Then, the measurement equation is obtained: （1） in, It is the measurement function of complex structural equipment, describing the measurement value and structural response under the condition of no measurement noise. the relationship between; express Simplified writing of ; Indicates the time value.

4. The reliability analysis method for complex structure equipment under measurement conditions according to claim 2 is characterized in that: The third step comprises the following steps: Step 3.1: Define the mechanical reliability indicators to be analyzed , the mechanical reliability index Yes Response is a function of uncertainty random variables function; therefore, Expressed as ; Step 3.2, solve the known measurement data conditions hour, The conditional probability density function of , It is expressed as: （2） in, for The joint probability density of The measured value The probability density of According to the law of conservation of probability, the joint probability density of the system consisting of the finite element model of complex structural equipment and the measurement conditions is Written as: （3） in, is the Dirac function, the function value is zero at all points except the zero point, and the integral over the entire domain is equal to 1; represents the joint probability density function of the measurement noise at all time steps, The definition of is as detailed in step 1.

3. This means that when the measurement noise at all time steps is exactly When , the corresponding value of the joint probability density function; pass For random variables and measurement noise The integral of the marginal probability density is , as shown in formula (4): （4） Again Points: （5） At this time, and Substitute as the numerator and denominator into the probability density function expression (2) to obtain the known measurement data condition hour, The conditional probability density function of .

5. The reliability analysis method for complex structure equipment under measurement conditions according to claim 1, characterized in that: The fourth step comprises the following steps: Step 4.1: Use the quasi-Monte Carlo method to solve This high-dimensional integral; First, a generalized low-bias sampling method is used to quantify the random variables in the complex structure equipment under consideration. Sampling is carried out; sampling follows The probability distribution of Sample points , and find the corresponding point set weight ; Will obtain Sample points Substituting into the finite element model of complex structural equipment, the corresponding Then, the measured value is calculated using the generalized quasi-Monte Carlo calculation format shown in formula (6) The probability density function of : （6） Step 4.2, use the Gaussian function to approximate the Dirac function, and then use the generalized quasi-Monte Carlo method to solve it. At this time, formula (4) is rewritten as: （7） Among them, when using Gaussian function approximation, represents the smoothness factor; Step 4.3, the obtained and Substituting into formula (2), The solution is complete.

6. The reliability analysis method for complex structure equipment under measurement conditions according to claim 1, characterized in that: The fifth step comprises the following steps: Step 5.1: Determine the normal use of the complex structure equipment under consideration according to the actual problem. The allowed threshold ; Step 5.2, the reliability probability of complex structure equipment is expressed as ,use , and numerically integrate and solve it to obtain the reliability probability of complex structure equipment, and complete the reliability analysis of complex structure equipment.

Images