A fatigue reliability evaluation method for capsule sensor considering multi-source uncertainty

Abstract

The present invention relates to the field of reliability design analysis, and specifically to a method for fatigue reliability assessment of a membrane box sensor that considers multi-source uncertainty. The main steps are as follows: (1) establishing a multi-source uncertainty characterization model for the membrane box sensor; (2) establishing a three-dimensional assembly model and a finite element model of the membrane box sensor; (3) establishing a fault physical model and a reliability model for the membrane box sensor; and (4) assessing the fatigue reliability of the membrane box sensor based on Monte Carlo simulation and a Kriging proxy model. The beneficial effects of the present invention are that it fully considers the influence of multi-source uncertainty, including pre-tension uncertainty, can effectively save a lot of simulation time, and can more efficiently and accurately assess the fatigue reliability of the membrane box sensor, providing theoretical methodological support for its reliability design, fault prediction, and maintenance and replacement decisions.

Description

Technical Field

[0001] The present invention relates to the field of reliability design analysis, and in particular to a fatigue reliability evaluation method for a membrane box sensor considering multi-source uncertainties. Background Art

[0002] Large-scale industrial processes and complex equipment systems present numerous potential hazards during long-term automated operation. Instrumentation, as the fundamental unit of measurement, control, and perception, is critical to their automated operation and control, and fundamentally guarantees their safe and reliable operation. Failure of an instrument can rapidly impact the operation of the entire system, leading to serious accidents, environmental damage, economic losses, and even casualties.

[0003] The rapid development of science and technology has led to an ever-increasing variety and variety of instrumentation. Instrumentation technology has entered a new era of electronicization, digitization, and intelligence. Intelligent instruments offer numerous advanced features, including self-diagnosis, error correction, remote communication, human-computer interaction, and data processing. These instruments enable more accurate and stable measurement and monitoring in increasingly complex environments. They are currently widely used in aerospace, railway transportation, hydropower, petrochemicals, and nuclear power. However, the powerful functionality of intelligent instruments inevitably comes with complex structures and cumbersome production processes, resulting in relatively low reliability. Therefore, ensuring the long-term stable and reliable operation of intelligent instruments, providing a solid foundation for large-scale industrial processes and complex equipment systems, has become a pressing issue.

[0004] Smart pressure transmitters are intelligent pressure parameter measurement instruments used to measure parameters such as differential pressure and pressure of various liquids and gases. They are one of the most representative products in smart instrumentation. Among the many components of a smart pressure transmitter, the diaphragm sensor plays a crucial role, converting the medium's pressure signal into an electrical signal. Its reliability directly impacts the reliability of the entire smart pressure transmitter. Under the pressure of the measured medium, the central measuring diaphragm in the diaphragm sensor will develop microcracks under the continuous impact of external pressure. Under the influence of alternating loads, these microcracks continue to initiat e, aggregate, and connect, eventually forming macrocracks that cause the central measuring diaphragm to rupture, ultimately damaging the entire smart pressure transmitter. Furthermore, the diaphragm sensor in a smart pressure transmitter is subject to uncertainties in its material, structure, and applied load. These uncertainties can cause performance fluctuations in the various components of the diaphragm sensor, ultimately affecting the failure behavior of the diaphragm sensor and the entire smart pressure transmitter. Among these uncertain parameters, pre-tension significantly affects the deflection of the pressure-sensing diaphragm. The magnitude of pre-tension is related to the diaphragm's subsequent mechanical properties, and the uniformity and consistency of its internal tension directly impact the accuracy and long-term stability of diaphragm measurements. Therefore, it is important to focus on the impact of pre-tension uncertainty on the diaphragm sensor. In this context, to design a high-precision, long-life intelligent pressure transmitter, it is necessary to develop a high-precision fatigue reliability assessment method for diaphragm sensors that fully accounts for multiple sources of uncertainty. This method can be used for reliability analysis and evaluation during the product design phase.

[0005] Based on the above background, this paper provides a fatigue reliability assessment method for capsule sensors that considers multiple sources of uncertainty. Monte Carlo simulation is combined with finite element simulation to evaluate the impact of multiple sources of uncertainty on capsule sensor fatigue failure. A Kriging proxy model is then used to reduce the computational time and resources of the finite element simulation, achieving an optimal balance between accuracy and efficiency. Summary of the Invention

[0006] To fully consider the impact of diaphragm pretension on the fatigue behavior of the central measuring diaphragm and more accurately assess the reliability of a capsule sensor under multi-source uncertainty, the present invention provides a capsule sensor fatigue reliability assessment method that considers multi-source uncertainty. This method effectively saves significant simulation time and resources, while fully accounting for the impact of multi-source uncertainty, including pretension uncertainty, and enables more efficient analysis and assessment of the fatigue reliability of capsule sensors. This method provides theoretical support for reliability design, fault prediction, and repair and replacement decisions for capsule sensors. It also has potential practical application in addressing complex and time-consuming reliability modeling and analysis problems.

[0007] To achieve the above-mentioned object, the present invention adopts the following technical solution: a fatigue reliability evaluation method of a capsule sensor considering multi-source uncertainty, comprising the following steps:

[0008] Step 1: Sort out the multi-source uncertainties faced by the membrane box sensor during its manufacturing, assembly and service, including material parameter uncertainty, assembly parameter uncertainty and load parameter uncertainty, and establish a probabilistic characterization model of the above parameters through probabilistic statistics methods.

[0009] Specifically, six key variables were selected from the material parameters, assembly parameters and load parameters for uncertainty analysis, namely: the elastic modulus E1 of the central measuring diaphragm material, the Poisson's ratio v1 of the central measuring diaphragm material, the elastic modulus E2 of the isolation diaphragm material, the Poisson's ratio v2 of the isolation diaphragm material, the medium pressure P, and the pre-tension T of the central measuring diaphragm.

[0010] For the pre-tension T of the central measuring diaphragm, in order to simulate the way the pre-tension is applied to the diaphragm during the actual assembly process, the effect of the pre-tension is simulated by applying radial deformation to the diaphragm. The pre-tension is equivalently converted into radial deformation using formula (1). The uncertainty of the pre-tension is reflected in the uncertainty of the radial expansion of the central measuring diaphragm during the actual assembly process:

[0011]

[0012] Where T is the pre-tension on the diaphragm; E is the elastic modulus of the diaphragm material; D is the diameter of the diaphragm; and ΔD is the equivalent radial expansion of the diaphragm.

[0013] Subsequently, the uncertainty of the pre-tension T, that is, the uncertainty of the radial expansion ΔD of the central measurement diaphragm, is characterized by the normal distribution. The probability density function of the normal distribution is shown in formula (2):

[0014]

[0015] Where μ is the mean of the normal distribution and σ is the standard deviation of the normal distribution.

[0016] Finally, the equivalent radial expansion ΔD of the theoretical design value of the pre-tension applied to the central measuring diaphragm during the actual assembly process is CL As the mean of the normal distribution, it determines the upper limit of the fluctuation of the radial expansion in the actual assembly process ΔD UCL and the lower limit of fluctuation ΔD LCL , and the standard deviation of the normal distribution is calculated based on the Six Sigma quality management method A normal distribution probability statistical model is established to characterize the uncertainty of pre-tension, namely

[0017] For the remaining five random variables, their respective nominal values ​​A CL As the mean of the normal distribution, the standard deviation of the normal distribution of the corresponding random variable is determined by using a coefficient of variation of 0.05, which is 0.05×A CL , a normal distribution probability statistical model is established to characterize the uncertainty of the material and load parameters, namely A~N(A CL ,(0.05A CL ) 2 ).

[0018] Step 2: Establish a three-dimensional assembly model of the membrane box sensor, perform meshing, impose degree of freedom constraints and load boundary conditions, and establish a finite element simulation model of the membrane box sensor.

[0019] Specifically, a three-dimensional assembly model of the isolation diaphragm, metal shell, central measuring diaphragm (solid structure) and silicone oil transmission medium (liquid structure) is established at the same time, and grid division is carried out. By applying load boundary conditions, the effect of external pressure is transferred to the central measuring diaphragm through silicone oil, thereby simulating the fatigue behavior of the central measuring diaphragm of the membrane box sensor under the action of external pressure.

[0020] Step 3: Define the fault physics model used to characterize the fatigue behavior of the diaphragm in the center of the capsule sensor, and thereby establish a reliability model of the capsule sensor.

[0021] Specifically, as shown in Equation (3), the Basquin-Coffin-Manson equation is a widely used failure physics model for fatigue life prediction. It can describe the fatigue life of materials under different strain amplitudes. This equation considers both low-cycle fatigue and high-cycle fatigue, so this failure mechanism model was chosen to characterize the fatigue behavior of the central measuring diaphragm of the capsule sensor.

[0022]

[0023] in, is the total strain amplitude; is the elastic strain amplitude; is the plastic strain amplitude; σ′ f is the fatigue strengthening coefficient; E is the elastic modulus of the material; b is the Basquin fatigue strength index; ε′ f is the fatigue ductility coefficient; c is the Coffin-Manson fatigue ductility index; N f is the fatigue life.

[0024] Furthermore, the reliability model of the membrane box sensor can be represented as a time-varying reliability function, as shown in formula (4):

[0025]

[0026] Among them, R(t) is the reliability function of the membrane box sensor, which represents the reliability at time t; N f is a random variable, which represents the fatigue life of the membrane box sensor under the influence of various uncertainty parameters; f(t) is the probability density function of the random variable.

[0027] Step 4: Monte Carlo simulation method and Kriging proxy model are used to evaluate the fatigue life distribution and fatigue reliability of the membrane capsule sensor, which includes the following steps:

[0028] Step 4.1: Based on the probability representation model of each uncertainty parameter established in step 1, perform Monte Carlo random sampling to generate an initial sample pool containing N1 groups of samples.

[0029] Specifically, each set of samples in the initial sample pool consists of six parameters: the elastic modulus E1 of the central measuring diaphragm material, the Poisson's ratio v1 of the central measuring diaphragm material, the elastic modulus E2 of the isolation diaphragm material, the Poisson's ratio v2 of the isolation diaphragm material, the medium pressure P, and the equivalent radial expansion ΔD of the pre-tensioned central measuring diaphragm. The initial sample pool can be expressed as:

[0030] Ω0={(E1 i ,v1 i ,E2 i ,v2 i ,P i ,ΔD i )|i∈N * ,i≤N1} (5)

[0031] Among them, Ω0 is the initial sample pool; (E1 i ,v1 i ,E2 i ,v2 i ,P i ,ΔD i ) is the i-th group of samples; N1 is the number of samples not less than 50.

[0032] Step 4.2: Substitute the N1 groups of random samples of each uncertain parameter generated in step 4.1 into the finite element model of the membrane box sensor established in step 2, carry out finite element simulation analysis of the membrane box sensor, and extract the maximum strain value of the central measurement diaphragm.

[0033] Specifically, the maximum strain value of the central measurement diaphragm in the finite element simulation results of the N1 group of samples in the initial sample pool can be expressed as:

[0034] Ω1={Δε t i |i∈N * ,i≤N1} (6)

[0035] Where Ω1 is the set of maximum strain values ​​of the initial sample pool; Δε t i is the maximum strain value of the i-th group of samples.

[0036] Step 4.3: Based on the fatigue model of the central measuring diaphragm established in step 3 and the maximum strain value of the central measuring diaphragm obtained in step 4.2, calculate the fatigue life of the membrane box sensor samples in group N1 respectively;

[0037] Specifically, the fatigue life of the N1 group of samples in the initial sample pool can be calculated using formula (3), which is expressed as:

[0038] Ω2={N f i |i∈N * ,i≤N1} (7)

[0039] Where Ω2 is the fatigue life of the initial sample pool; N f i is the fatigue life of the i-th group of samples.

[0040] Step 4.4: Use the uncertainty parameters of the N1 group samples obtained in step 4.3 and the corresponding fatigue life to construct the Kriging proxy model.

[0041] Specifically, a Kriging proxy model is constructed with Ω0 as the sample feature and Ω2 as the sample response.

[0042] Step 4.5: Based on the probability representation model of each uncertainty parameter established in step 1, Monte Carlo random sampling is performed to generate a candidate sample pool containing N2 group samples, and the Kriging model constructed in step 4.4 is used to predict the fatigue life of the N2 group samples in the candidate sample pool.

[0043] Specifically, each set of samples in the candidate sample pool consists of six parameters: the elastic modulus E1 of the central measurement diaphragm material, the Poisson's ratio v1 of the central measurement diaphragm material, the elastic modulus E2 of the isolation diaphragm material, the Poisson's ratio v2 of the isolation diaphragm material, the medium pressure P, and the equivalent radial expansion ΔD of the pre-tensioned central measurement diaphragm. The candidate sample pool can be expressed as:

[0044] Ω3={(E1 i ,v1 i ,E2 i ,v2 i ,P i ,ΔD i )|i∈N * ,i≤N2} (8)

[0045] Among them, Ω3 is the candidate sample pool; (E1i ,v1 i ,E2 i ,v2 i ,P i ,ΔD i ) is the i-th group of samples; N2 is the number of samples not less than 5000.

[0046] Furthermore, the fatigue life of the N2 group of samples in the candidate sample pool predicted by the Kriging model can be expressed as:

[0047] Ω4={N f i |i∈N * ,i≤N2} (9)

[0048] Where Ω4 is the set of predicted values ​​of fatigue life of candidate sample pool; N f i is the predicted value of fatigue life of the i-th group of samples.

[0049] Step 4.6: Use the fatigue life of the N2 group of samples in the candidate sample pool obtained in step 4.5 to draw a frequency-fatigue life histogram, and use the reliability model established in step 3 to evaluate the fatigue life distribution and fatigue reliability of the membrane box sensor.

[0050] Specifically, as shown in formula (10), the kernel density function is used to evaluate the probability density function of the fatigue life of the membrane box sensor:

[0051]

[0052] in, is the probability density function estimate of the fatigue life of the membrane sensor; N2 is the number of samples in the candidate sample pool; N fi is the fatigue life of the i-th group of samples in the candidate sample pool; h is the bandwidth; K(·) is the kernel function, and the normal kernel function is generally used, and its expression is as follows:

[0053]

[0054] Subsequently, the fatigue reliability of the membrane box sensor is evaluated using the reliability model established in step 3. The evaluation results are as follows:

[0055]

[0056] The present invention has the following beneficial effects:

[0057] 1. This invention provides a fatigue reliability assessment method for capsule sensors that considers multiple sources of uncertainty. This method fully accounts for the impact of diaphragm pretension on the fatigue behavior of the central measuring diaphragm. This method can more accurately assess the reliability level of capsule sensors under multiple sources of uncertainty and provide theoretical support for reliability design, fault prediction, and repair and replacement decisions for capsule sensors.

[0058] 2. The present invention provides a fatigue reliability evaluation method for a membrane box sensor that takes into account multi-source uncertainty. Under the premise of fully considering the influence of multi-source uncertainty including pre-tension uncertainty, it can effectively save a lot of simulation time and resources, and more efficiently analyze and evaluate the fatigue reliability of the membrane box sensor. It has potential practical application value in dealing with highly complex and time-consuming reliability modeling and analysis problems. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 This is a flow chart of a fatigue reliability evaluation method for a capsule sensor considering multi-source uncertainty proposed by the present invention;

[0060] Figure 2 It is a three-dimensional geometric assembly model of the membrane box sensor of the intelligent pressure transmitter in the embodiment of the present invention;

[0061] Figure 3 It is the grid division result of the membrane box sensor of the intelligent pressure transmitter in the embodiment of the present invention;

[0062] Figure 4 Schematic diagram of boundary conditions in a finite element model of a diaphragm sensor of an intelligent pressure transmitter in an embodiment of the present invention;

[0063] Figure 5 Schematic diagram of pre-tension applied to the central measuring diaphragm in an embodiment of the present invention;

[0064] Figure 6 is the fatigue life of 50 groups of samples in the initial sample pool in the embodiment of the present invention;

[0065] Figure 7 It is the fatigue life probability density function and reliability function of the membrane box sensor of the intelligent pressure transmitter in the implementation case of the present invention. DETAILED DESCRIPTION

[0066] The present invention is further described below with reference to the accompanying drawings and specific implementation examples.

[0067] This implementation case takes the diaphragm sensor of a certain type of intelligent pressure transmitter as the analysis object. Figure 1The method flow shown in the figure applies a fatigue reliability assessment method for capsule sensors that considers multiple sources of uncertainty, as proposed by the present invention. This implementation case specifically includes the following:

[0068] 1. Probabilistic representation modeling of multi-source uncertainty of membrane box sensors

[0069] This study examined the multiple sources of uncertainty faced by capsule sensors during their manufacturing, assembly, and service life, including material parameter uncertainty, assembly parameter uncertainty, and load parameter uncertainty. Specifically, six key variables were selected from these three parameters for uncertainty analysis: the elastic modulus E1 of the central measuring diaphragm material, the Poisson's ratio v1 of the central measuring diaphragm material, the elastic modulus E2 of the isolation diaphragm material, the Poisson's ratio v2 of the isolation diaphragm material, the medium pressure P, and the central measuring diaphragm preload tension T.

[0070] For the pre-tension T of the central measuring diaphragm, in order to simulate the way the pre-tension is applied to the diaphragm during the actual assembly process, the effect of the pre-tension is simulated by applying radial deformation to the diaphragm. The pre-tension is equivalently converted into radial deformation using formula (13). The uncertainty of the pre-tension is reflected in the uncertainty of the radial expansion of the central measuring diaphragm during the actual assembly process:

[0071]

[0072] Where T is the pre-tension on the diaphragm; E is the elastic modulus of the diaphragm material; D is the diameter of the diaphragm; and ΔD is the equivalent radial expansion of the diaphragm.

[0073] Subsequently, the uncertainty of the pre-tension T, that is, the uncertainty of the radial expansion ΔD of the central measurement diaphragm, is characterized by the normal distribution. The probability density function of the normal distribution is shown in Equation (14):

[0074]

[0075] Where μ is the mean of the normal distribution and σ is the standard deviation of the normal distribution.

[0076] Finally, the theoretical design value T of the pre-tension applied to the central measuring diaphragm during the actual assembly process is CL =Equivalent radial expansion ΔD of 44MPa CL =0.0066mm as the mean of the normal distribution, and the upper limit of the fluctuation of the radial expansion in the actual assembly process ΔD is determined based on engineering experience UCL =0.0076mm and fluctuation lower limit ΔD LCL =0.0056mm, and the standard deviation of the normal distribution is calculated based on the Six Sigma quality management method A normal distribution probability statistical model is established to characterize the uncertainty of pre-tension, namely ΔD~N(0.0066,(3.3×10 -4 ) 2 ).

[0077] For the remaining five random variables, their respective nominal values ​​A CL As the mean of the normal distribution, the standard deviation of the normal distribution of the corresponding random variable is determined by using a coefficient of variation of 0.05, which is 0.05×A CL , a normal distribution probability statistical model is established to characterize the uncertainty of the material and load parameters, namely A~N(A CL ,(0.05A CL ) 2 ). The probability representation models of the above six random variables are shown in Table 1.

[0078] Table 1 Probabilistic representation model of multi-source uncertainty of diaphragm sensor of intelligent pressure transmitter

[0079]

[0080] 2. Establishment of 3D assembly model and finite element model of membrane box sensor

[0081] (1) Establishment of three-dimensional geometric assembly model: The membrane box sensor consists of the same corrugated isolation diaphragm on both sides, a metal shell and a central measuring diaphragm, and is filled with silicone oil as the transmission medium. The three-dimensional geometric assembly model of the membrane box sensor is established based on SolidWorks software, as shown in the figure. Figure 2 The specific dimensions of the isolation diaphragm and the measuring diaphragm are shown in Table 2.

[0082] Table 2 Specific dimensions of the isolation diaphragm and the measuring diaphragm

[0083]

[0084] (2) Meshing: ANSYS Workbench 19.1 was used to mesh the diaphragm sensor. Since the isolation diaphragm and the measuring diaphragm are the key components of the diaphragm sensor’s pressure transmission, a finer mesh was used to mesh the isolation diaphragm and the measuring diaphragm to improve the calculation accuracy. The meshing results of the components of the diaphragm sensor are shown in the figure below. Figure 3 shown.

[0085] (3) Freedom constraints and load boundary conditions: Figure 4As shown in the figure, to simulate the installation of the diaphragm sensor inside the intelligent pressure transmitter, a fixed constraint is first applied to the circumferential surface of the metal shell; then, a radial displacement is applied to the central measuring diaphragm to simulate the pre-tension of the diaphragm sensor during the actual assembly process; next, a pressure of 0.2 MPa is applied to one end of the isolation diaphragm to simulate the effect of the medium pressure load; finally, a binding contact is applied between the components of the diaphragm sensor to simulate the actual assembly relationship.

[0086] 3. Establishment of the physical model and reliability model of the membrane box sensor failure

[0087] The failure physics model used to characterize the fatigue behavior of the center measuring diaphragm of the capsule sensor is clearly defined. Specifically, as shown in Equation (15), the Basquin-Coffin-Manson equation is a failure physics model widely used in fatigue life prediction. It can describe the fatigue life of materials under different strain amplitudes. This equation considers both low-cycle fatigue and high-cycle fatigue, so this failure mechanism model is chosen to characterize the fatigue behavior of the center measuring diaphragm of the capsule sensor.

[0088]

[0089] in, is the total strain amplitude; is the elastic strain amplitude; is the plastic strain amplitude; σ′ f is the fatigue strengthening coefficient; E is the elastic modulus of the material; b is the Basquin fatigue strength index; ε′ f is the fatigue ductility coefficient; c is the Coffin-Manson fatigue ductility index; N f is the fatigue life.

[0090] Furthermore, a reliability model of the membrane box sensor is established, which can be represented as a time-varying reliability function, as shown in formula (16):

[0091]

[0092] Among them, R(t) is the reliability function of the membrane box sensor, which represents the reliability at time t; N f is a random variable, which represents the fatigue life of the membrane box sensor under the influence of various uncertainty parameters; f(t) is the probability density function of the random variable.

[0093] 4. Fatigue reliability assessment of membrane sensor based on Monte Carlo simulation and Kriging proxy model

[0094] (1) Initial sample pool generation: Based on the established probability representation model of each uncertainty parameter, Monte Carlo random sampling is performed to generate an initial sample pool containing 50 groups of samples. The initial sample pool can be expressed as:

[0095] Ω0={(E1 i ,v1 i ,E2 i ,v2 i ,P i ,ΔD i )|i∈N * ,i≤50} (17)

[0096] Among them, Ω0 is the initial sample pool; (E1 i ,v1 i ,E2 i ,v2 i ,P i ,ΔD i ) is the i-th group of samples.

[0097] (2) Finite element simulation: Based on the established finite element model, finite element simulations were carried out for 50 groups of samples in Ω0, and the maximum strain value of the central measurement diaphragm in the simulation results was extracted, which can be expressed as:

[0098] Ω1={Δε t i |i∈N * ,i≤50} (18)

[0099] Where Ω1 is the set of maximum strain values ​​of the initial sample pool; Δε t i is the maximum strain value of the i-th group of samples.

[0100] (3) Fatigue life calculation: Based on the fault physics model of formula (15), assuming that the pressure on the membrane box sensor acts once per minute, the fatigue life of 50 groups of samples in Ω0 is calculated respectively, as follows: Figure 6 As shown, it can be expressed as:

[0101] Ω2={N f i |i∈N * ,i≤50} (19)

[0102] Where Ω2 is the fatigue life of the initial sample pool; N f i is the fatigue life of the i-th group of samples.

[0103] (4) Kriging model construction: The Kriging proxy model is constructed with Ω0 as the sample feature and Ω2 as the sample response.

[0104] (5) Generation of candidate sample pool and fatigue life prediction: Based on the established probability representation model of each uncertainty parameter, Monte Carlo random sampling is performed to generate a candidate sample pool containing 10,000 groups of samples, and the fatigue life of the 10,000 groups of samples in the candidate sample pool is predicted using the constructed Kriging model.

[0105] (6) Fatigue life distribution and fatigue reliability evaluation: Using the fatigue life of 10,000 groups of samples in the candidate sample pool, a frequency-fatigue life histogram is drawn, and the kernel density function is used to evaluate the probability density function of the fatigue life of the membrane box sensor:

[0106]

[0107] in, is the probability density function estimate of the fatigue life of the membrane sensor; N2 is the number of samples in the candidate sample pool, N2 = 10000; N fi is the fatigue life of the i-th group of samples in the candidate sample pool; h is the bandwidth, h = 125.77; K(·) is the kernel function, and the normal kernel function is generally used, and its expression is as follows:

[0108]

[0109] Then, if Figure 7 As shown in Figure 1, the fatigue reliability of the membrane box sensor is evaluated using the reliability model of formula (16). The evaluation results are as follows:

[0110]

[0111] It can be seen from the calculation results that the fatigue reliability evaluation method of the membrane box sensor considering multi-source uncertainty proposed in the present invention can quickly evaluate the reliability level of the membrane box sensor.

[0112] Parts of the present invention that are not disclosed in detail belong to the common knowledge in the art.

[0113] Although the above describes the illustrative specific embodiments of the present invention to facilitate understanding of the present invention by those skilled in the art, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the appended claims, these changes are obvious, and all inventions and creations using the concepts of the present invention are protected.

Claims

1. A fatigue reliability assessment method for capsule sensors considering multi-source uncertainty, characterized in that: The following steps are involved: Step 1: Establish a probabilistic representation model of the uncertainty of the membrane box sensor material parameters, load parameters, and assembly parameters through probabilistic statistical methods, which specifically includes the following steps: Step 1.1: Sort out the material parameter uncertainties and load parameter uncertainties in the manufacturing and service process of the membrane capsule sensor, and establish a probabilistic representation model of the above parameters through probabilistic statistical methods; Step 1.2: Sort out the uncertainty of the assembly parameters in the membrane box sensor assembly process, and establish a probabilistic representation model of the above parameters through probabilistic statistics methods; Step 2: Establish a three-dimensional assembly model of the membrane box sensor, perform meshing, apply degree of freedom constraints and load boundary conditions, and establish a finite element simulation model of the membrane box sensor; Step 3: Establish a fatigue model of the central measurement diaphragm in the form of formula (1) and a reliability model of the membrane box sensor in the form of formula (2); in: is the total strain amplitude; is the elastic strain amplitude; is the plastic strain amplitude; σ′ f is the fatigue strengthening coefficient; E is the elastic modulus of the material; b is the Basquin fatigue strength index; ε′ f is the fatigue ductility coefficient; c is the Coffin-Manson fatigue extension index; N f is fatigue life; in: R(t) is the reliability function of the membrane box sensor, which represents the reliability at time t; N f is a random variable, which represents the fatigue life of the central measurement diaphragm under the influence of various uncertainty parameters; f(t) is the probability density function of the random variable; Step 4: Monte Carlo simulation method and Kriging proxy model are used to evaluate the fatigue life distribution and fatigue reliability of the membrane capsule sensor, which includes the following steps: Step 4.1: Based on the probability representation model of each uncertainty parameter established in step 1, perform Monte Carlo random sampling to generate an initial sample pool containing N1 groups of samples; Step 4.2: Substitute the N1 groups of random samples of each uncertain parameter generated in step 4.1 into the finite element model of the membrane box sensor established in step 2, carry out finite element simulation analysis of the membrane box sensor, and extract the maximum strain value of the central measurement diaphragm; Step 4.3: Based on the fatigue model of the central measuring diaphragm established in step 3 and the maximum strain value of the central measuring diaphragm obtained in step 4.2, calculate the fatigue life of the membrane box sensor samples in group N1 respectively; Step 4.4: Use the uncertainty parameters of the N1 group samples obtained in step 4.3 and the corresponding fatigue life to construct the Kriging proxy model; Step 4.5: Based on the probability representation model of each uncertainty parameter established in step 1, perform Monte Carlo random sampling to generate a candidate sample pool containing group N2 samples, and use the Kriging model constructed in step 4.4 to predict the fatigue life of group N2 samples in the candidate sample pool; Step 4.6: Use the fatigue life of the N2 group of samples in the candidate sample pool obtained in step 4.5 to draw a frequency-fatigue life histogram, and use the reliability model established in step 3 to evaluate the fatigue life distribution and fatigue reliability of the membrane box sensor.

2. The fatigue reliability evaluation method of a capsule sensor considering multi-source uncertainty according to claim 1 is characterized in that: Step 1.1 is used to comb the uncertainty of material parameters and load parameters in the manufacturing and service process of the membrane box sensor, and to establish a probabilistic representation model of the above parameters through probabilistic statistical methods, which specifically includes the following steps: Step 1.1.1: Take the nominal value A of each material and load parameter of the capsule sensor in actual manufacturing and service process CL as the mean of a normal distribution; Step 1.1.2: Take the coefficient of variation as 0.05 and calculate the standard deviation of the normal distribution as 0.05×A CL ; Step 1.1.3: Establish a normal distribution probability statistical model to characterize the uncertainty of the material and load parameters, namely: A~N(A CL ,(0.05A CL ) 2 ).

3. The fatigue reliability evaluation method of a capsule sensor considering multi-source uncertainty according to claim 1 is characterized in that: The uncertainty of the assembly parameters in the process of assembling the membrane box sensor described in step 1.2 is combed, and a probability representation model of the above parameters is established by a probability statistics method, which specifically includes the following steps: Step 1.2.1: Simulate the effect of pre-tension by applying radial deformation to the diaphragm. Use Equation (3) to convert the pre-tension into radial deformation. The uncertainty of pre-tension is reflected in the uncertainty of the radial expansion of the diaphragm measured in the actual assembly process: in: T is the magnitude of the pre-tension on the measuring diaphragm; E is the elastic modulus of the measured diaphragm material; D is the diameter of the measuring diaphragm; ΔD is the equivalent radial expansion of the measured diaphragm; Step 1.2.2: Use the normal distribution to characterize the uncertainty of the preload, i.e., the uncertainty of the radial expansion of the central measurement diaphragm; Step 1.2.3: Calculate the equivalent radial expansion ΔD of the theoretical design value of the pre-tension applied to the center diaphragm during the actual assembly process. CL as the mean of a normal distribution; Step 1.2.4: Determine the upper limit of radial expansion fluctuation ΔD during the actual assembly process UCL and the lower limit of fluctuation ΔD LCL , and the standard deviation of the normal distribution is calculated based on the Six Sigma quality management method Step 1.2.5: Establish a normal distribution probability statistical model to characterize the uncertainty of pre-tension, namely:

4. The fatigue reliability evaluation method of a capsule sensor considering multi-source uncertainty according to claim 1 is characterized in that: The fatigue life distribution and fatigue reliability of the capsule sensor are evaluated as described in step 4.6, specifically: As shown in formula (4), the kernel density function is used to evaluate the probability density function of the fatigue life of the membrane box sensor: in: is the probability density function estimate of the fatigue life of the membrane sensor; N2 is the number of samples in the candidate sample pool; N fi is the fatigue life of the i-th group of samples in the candidate sample pool; h is the bandwidth; K(·) is the kernel function; Subsequently, the fatigue reliability of the membrane box sensor is evaluated using the reliability model established in step 3. The evaluation results are as follows: 。

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