Non-probabilistic reliability analysis method for underwater manipulator considering fluid-structure coupling effect

Abstract

This invention belongs to the field of underwater manipulator reliability analysis technology, and discloses a non-probabilistic reliability analysis method for underwater manipulators considering fluid-structure interaction effects. The method includes the following steps: quantifying the uncertainty of fluid load parameters under finite sample conditions using a non-probabilistic interval method; updating sample points based on Bayesian theory, and obtaining the relationship between interval parameters and reliability through analytical solutions; conducting strength and stability analysis of underwater manipulator components using the buckling stability criterion as the failure criterion to obtain the critical buckling load; performing uncertainty propagation analysis using the Taylor series expansion method to solve for the structural response interval corresponding to the non-probabilistic interval of the input uncertainty parameters; and comparing the response interval with the limit state equation using stress-strength interference theory or tolerance interference theory to establish a non-probabilistic Bayesian reliable reliability analysis model, suitable for reliability assessment of underwater manipulator components under small sample conditions.

Description

Technical Field

[0001] This invention relates to the field of underwater robotic arm reliability analysis technology, and in particular to a nonprobabilistic reliability analysis method for underwater robotic arms that considers fluid-structure interaction effects. Background Technology

[0002] As the core actuator for tasks such as deep-sea exploration, marine resource development, and underwater facility installation and maintenance, the structural reliability of underwater robotic arms directly determines the success or failure and economic cost of the entire operation system. Unlike industrial robots on land or in fixed environments, underwater robotic arms operate in extremely harsh and unpredictable marine environments, continuously enduring hydrostatic pressure, chemical corrosion, biofouling, and the most complex unsteady and random hydrodynamic loads.

[0003] In engineering practice, structural failure is usually not caused by insufficient static strength, but by dynamic instability. One key failure mode often overlooked in preliminary design is flow-induced buckling. When robotic arm components deploy in ocean currents or encounter transient currents (such as internal waves or vortices), the hydrodynamic forces acting on the arm create complex pressure fields and shear forces, generating enormous compressive stress within the structure. Once this compressive stress exceeds a certain critical threshold, the structure will buckle—that is, undergo a sudden large geometric deformation and lose stability, leading to loss of control of the entire robotic arm component or structural failure. This instability is sudden and extremely destructive.

[0004] In traditional structural analysis, designers treat structural parameters, material properties, and external loads as deterministic quantities, employing deterministic models for analysis. However, in practical engineering, underwater robotic arm components face numerous uncertainties, including the dispersion of material properties, manufacturing process deviations, unsteady loads, uncertainties in hydrodynamic coefficients, and errors introduced by model simplification. If these uncertainties are not properly quantified, reliability assessments will deviate from reality, thus affecting structural safety. Traditional probabilistic reliability methods rely on large amounts of sample data to construct accurate probability distributions, but in the field of underwater robotic arm components, demanding experimental conditions and scarce samples make it difficult to meet the requirements of probabilistic models.

[0005] Therefore, this invention uses a non-probabilistic interval method to quantify the uncertainty of material and load parameters, uses a uniform distribution as the prior distribution of the interval radius, and combines a Bayesian update mechanism to construct a credible non-probabilistic reliability analysis model, which is suitable for reliability assessment of underwater robotic arm component structures under small sample conditions. Summary of the Invention

[0006] The purpose of this invention is to provide a non-probabilistic reliability analysis method for underwater robotic arms that considers fluid-structure interaction effects. This method fully considers the uncertainty of the incoming flow velocity in the working environment of the underwater robotic arm's link structure. Based on Bayesian theory, a uniform distribution is used as the prior distribution of the interval radius. New sample points are introduced to update the interval radius, establishing a connection between the non-probabilistic quantification set and the credibility level. Combined with the maximum principal stress failure criterion, the critical failure equation of the system is solved using the Taylor series expansion method. A non-probabilistic credibility analysis model containing interval uncertainties is established. The obtained results contain credibility indicators, are more consistent with real-world conditions, and have stronger engineering applicability.

[0007] To achieve the above objectives, this invention provides a non-probabilistic reliability analysis method for underwater robotic arms considering fluid-structure interaction effects, comprising the following steps: Step S1: Derive the dynamic response relationship of the underwater robotic arm link structure under fluid-structure interaction, and use the non-probabilistic interval method to quantify the uncertainty of fluid load parameters under finite sample conditions; Step S2: Based on Bayesian theory, it is assumed that the interval parameter is an uncertain parameter that follows a uniform distribution. Sample points are introduced for updating, and the relationship between the interval parameter and the confidence level is obtained through analytical solution. Step S3: Considering the failure mode of the member under compression, the buckling stability criterion is used as the failure criterion to carry out the structural strength and stability analysis of the underwater robotic arm member and obtain the critical buckling load. Step S4: Use the Taylor series expansion method to perform uncertainty propagation analysis and solve for the structural response interval corresponding to the non-probability interval of the input uncertainty parameter; Step S5: Combining stress-intensity interference theory or tolerance interference theory, compare the response interval with the limit state equation to establish a nonprobabilistic Bayesian reliable analysis model.

[0008] Preferably, in step S1, the stream function and velocity potential of the flow around the cylinder are solved according to the potential flow theory, as shown below: (1); Applying Bernoulli's equation, we have: (2); pressure coefficient The expression is: (3); The final pressure coefficient can be obtained by combining formulas (1)-(3). The expression is as follows: (4); in, The tangential velocity of the cylindrical surface; The incoming flow velocity; For incoming static pressure; For fluid density; Surface pressure; Pressure coefficient; angle The calculation starts from the point directly opposite the incoming flow.

[0009] Preferably, in step S1, a load under arbitrary lateral load is considered. and axial force For members under combined action, take a small segment. Analysis is performed, and the torque balance equation for the rear end point of the micro-segment is as follows: (5); in, The bending moment is the bending moment at the left cross-section of the micro-segment; This is the differential increment of the bending moment; The shear force is the force on the left side of the micro-segment. This represents the differential increment of the shear force; For any lateral distributed load acting on the member; This refers to the constant axial pressure acting on the end of the member; Let x be the lateral deflection of the member perpendicular to its axis at coordinate x; The lateral deflection of the right side of the micro-segment perpendicular to the axis of the member; After simplification, it is considered The torque balance equations after the effect are as follows: (6); in, For the differential increment of deflection; By introducing the constitutive relations of the material and the moment-curvature equation of the beam, we further obtain: (7); in, The Young's modulus of the rod material; Let be the moment of inertia of the cross section of the rod about the neutral axis; Introducing amplification factor As shown below: (8); in, This is the theoretical limit load.

[0010] Preferably, in step S1, a non-probabilistic interval mathematical method is used to describe the uncertainty. According to interval mathematics theory, the uncertainty parameter is expressed in the form of an interval variable, as shown below: (9); in, For an interval vector of uncertain mechanical parameters; and These are the corresponding lower and upper bounds, respectively; It is the i-th component of the vector; and These are the lower and upper bounds, respectively; m is the number of uncertain mechanical parameters; According to interval mathematics theory, equation (9) can be rewritten in the form of center value and radius, as shown below: (10); (11); in, For the nominal value of the interval, The radius of the interval; For interval variables of uncertain mechanical parameters, it is the complete interval expression of uncertain mechanical parameters; For the first i The nominal values ​​of an uncertain mechanical parameter component within an interval; For the first i The radius of the interval of an uncertain mechanical parameter component; Considering the incoming flow velocity as an uncertain parameter, then we have: (12); Therefore, the uncertain incoming flow parameters are quantified into interval variables using the non-probabilistic interval method.

[0011] Preferably, in step S2, according to Bayesian theory, the posterior probability density of the interval parameters is as follows: (13); in, This represents the posterior probability density. This represents the prior probability density. The sampling density of the sample; Let be a normalization constant, representing the marginal density of the sample; Using the average distribution as the prior distribution for the interval radius, the probability density function of the uniform distribution is as follows: (14); in, , The upper and lower boundaries; The interval method assumes that all samples are equally likely to be distributed in the interval. Samples are drawn from a uniform distribution, and the sampling density is as follows: (15); in, These are the unknown parameters of the target to be estimated in Bayesian inference. From this, we can derive the expression for the posterior probability density, as shown below: (16); in, The independent sample size inferred from the Bayesian parameters; Given credibility Integrating over the posterior distribution, as shown below: (17); Finally, the numerical solution for the interval parameters under a given confidence level is obtained, as shown below: (18); in, To achieve a given level of confidence Under the given conditions, the Bayesian confidence upper bound of the interval radius of the uncertain mechanical parameters obtained by solving through the Bayesian posterior distribution.

[0012] Preferably, in step S3, a buckling stability criterion that distinguishes failure modes is used to perform static strength analysis of the composite material structure. For the buckling failure mode of the member, the buckling stability criterion is as follows: (19); in, This is referred to as the critical load, and in this invention, it is used as the ultimate buckling load. The elastic modulus of the material; The moment of inertia of the circular cross-section of the rod structure; For a considerable length; coefficient This is called the length factor, which characterizes the influence of the support method on the critical load. In finite element analysis, the surface pressure of the member obtained by CFD calculation in flow fields with different incoming velocities is used as the prestress for subsequent buckling analysis. Under the constraint condition that one end of the member is fixed and the other end is free, the load multiplier can be obtained by applying a pressure load. ; Failure coefficient for constructing buckling criteria As shown below: (20); Construct the limit state equations when When the applied load does not reach the buckling load of the member, the structure is considered safe; when When the applied load exceeds the critical instability load, the structure is determined to buckle and become unstable.

[0013] Preferably, in step S4, uncertainty propagation analysis is performed using the Taylor series expansion method to solve for the failure coefficient response interval under buckling failure conditions. The specific process is as follows: Let the response function of the structure be: (twenty one); Among them, the response function The state equation is the buckling stability criterion. A first-order Taylor expansion of the response function is performed, and the response bound of the response function over the entire interval is evaluated using information from the nominal value points and / or the endpoints of the interval containing the uncertainty parameter, as shown below: (twenty two); in, These are the upper and lower bounds of the interval for the response function, respectively. The nominal value of the interval point response function; This is the first derivative of the response function with respect to each uncertainty variable.

[0014] Preferably, in step S5, the response interval is compared with the limit state equation by combining the stress intensity interference theory, and a non-probabilistic Bayesian reliable analysis model is established. The specific process is as follows: Based on the interval stress-strength interference model, the reliability of the failure coefficient for structural buckling instability is obtained as follows: response range [ , Afterwards, it was compared with the critical value of the failure coefficient to obtain a confidence level of [value missing]. Structural failure probability As shown below: (twenty three); The credibility is then The structural reliability is: (twenty four); in, For credibility Structural failure probability under certain conditions; For credibility The lower bound of the failure coefficient response range for buckling instability of an underwater robotic arm structure under certain conditions; For credibility The upper bound of the failure coefficient response range for buckling instability of an underwater robotic arm structure under certain conditions; For credibility Nonprobabilistic reliability of underwater robotic arm structures considering fluid-structure interaction effects under certain conditions.

[0015] Therefore, this invention employs the aforementioned non-probabilistic reliability analysis method for underwater manipulators considering fluid-structure interaction effects. It establishes a reliability analysis model with credibility for interval uncertainty quantification of underwater manipulator link structures under fluid-structure interaction, considering multi-source uncertainties. Addressing the problem of inaccurate reliability assessment due to insufficient input variable sample information, based on Bayesian theory and interval models, the interval radius is considered to be an uncertain parameter of a prior distribution following a uniform distribution. The relationship between the interval radius and the credibility level is obtained through theoretical solutions. Taylor series expansion is used, combined with buckling stability criteria, to calculate the structural credibility and reliability. Simulation results show that the proposed non-probabilistic Bayesian model with a prior uniform distribution can better handle the balance between conservatism and credibility of the interval model. With the introduction of new sample points, the reliability will continuously improve, providing greater design space for the design of underwater manipulator link structures considering the influence of incoming flow velocity.

[0016] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0017] Figure 1 This is a flowchart of a nonprobabilistic reliability analysis method for an underwater robotic arm considering fluid-structure interaction effects, according to the present invention. Figure 2 This is a dimensional schematic diagram of a typical underwater robotic arm component structure of the present invention; Figure 3 This invention relates to the posterior distribution and posterior interval of the incoming flow velocity in the prior distribution, where the distribution is uniform. Figure 4 This invention describes the change of the interval radius update value with confidence level under the condition that the inflow velocity is uniformly distributed in the prior a priori sense. Figure 5 The invention relates to the change in nonprobabilistic reliability of the underwater robotic arm component structure with a prior uniform distribution as a function of credibility. Detailed Implementation

[0018] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0019] like Figure 1 As shown, this invention provides a non-probabilistic reliability analysis method for underwater robotic arms considering fluid-structure interaction effects. This method is used for the design and reliability analysis of structural members in underwater robotic arms and includes the following steps: Step S1: Derive the dynamic response relationship of the underwater robotic arm link structure under fluid-structure interaction, and use the non-probabilistic interval method to quantify the uncertainty of fluid load parameters (mainly considering the incoming flow velocity) under finite sample conditions; Step S2: Based on Bayesian theory, it is assumed that the interval parameter is an uncertain parameter that follows a uniform distribution. Sample points are introduced for updating, and the relationship between the interval parameter and the confidence level is obtained through analytical solution. Step S3: Considering the failure mode of the member under compression, the buckling stability criterion is used as the failure criterion to carry out the structural strength and stability analysis of the underwater robotic arm member and obtain the critical buckling load. Step S4: Use the Taylor series expansion method to perform uncertainty propagation analysis and solve for the structural response interval corresponding to the non-probability interval of the input uncertainty parameter; Step S5: Combining stress-intensity interference theory or tolerance interference theory, compare the response interval with the limit state equation to establish a nonprobabilistic Bayesian reliable analysis model.

[0020] Example 1 Step S1: Use the non-probabilistic interval method to obtain the non-probabilistic quantization set under the uncertainty of external load on the underwater robotic arm component structure.

[0021] Step S11: Based on potential flow theory, accurately solve for the stream function and velocity potential of the flow around the cylinder, as shown below: (1); Applying Bernoulli's equation, we have: (2); pressure coefficient The expression is: (3); The final pressure coefficient can be obtained by combining formulas (1)-(3). The expression is as follows: (4); in, The tangential velocity of the cylindrical surface; The incoming flow velocity; For incoming static pressure; For fluid density; Surface pressure; Pressure coefficient; angle The calculation starts from the point directly opposite the incoming flow.

[0022] Step S12 The axial compressive stress effect is a geometrical nonlinear effect in structural engineering. It describes the effect of axial compressive stress (ASU). ) in the lateral displacement of the structure ( Additional bending moment will be generated on ) This bending moment further increases the lateral displacement, forming a self-amplifying feedback loop. As a result, the internal forces and deformation of the structure are significantly increased, while its effective stiffness and stability are reduced. Consequently, when the actual load is much lower than the theoretical buckling load, the structure may fail due to uncontrolled deformation or material yielding.

[0023] Consider a load under arbitrary lateral direction. and axial force For members under combined action, take a small segment. Analysis is performed, and the torque balance equation for the rear end point of the micro-segment is as follows: (5); in, The bending moment is the bending moment at the left cross-section of the micro-segment; This is the differential increment of the bending moment; The shear force is the force on the left side of the micro-segment. This represents the differential increment of the shear force; For any lateral distributed load acting on the member; This refers to the constant axial pressure acting on the end of the member; Let x be the lateral deflection of the member perpendicular to its axis at coordinate x; The lateral deflection on the right side of the micro-segment is perpendicular to the axis of the rod.

[0024] Simplifying the above equation and ignoring higher-order minor quantities, we can obtain the following: The torque balance equations after the effect are as follows: (6); in, This is the differential increment of the deflection.

[0025] By introducing the constitutive relations of the material and the moment-curvature equation of the beam, we can further obtain: (7); in, The Young's modulus of the rod material; Let be the moment of inertia of the cross section of the rod about the neutral axis.

[0026] Introducing amplification factor As shown below: (8); in, This is the theoretical limit load.

[0027] In the problem of bar buckling failure, the transverse uniformly distributed load Initial deformation is provided. Under axial force... When it increases, The effect will amplify it. Therefore, when the member reaches the theoretical limit load... Previously, its actual deformation may have already exceeded the material limit or usage requirements, thus reducing its critical yield load from a practical perspective.

[0028] Step S13: Due to the uncertainty of the underwater vehicle's speed during actual service, the mechanical properties of the strut structure are dispersed. Depending on the amount of sample data, there are various methods to describe the uncertainty. Since the sample data for the underwater vehicle's robotic arm's working conditions and related mechanical properties is relatively small, a non-probabilistic interval mathematical method is suitable for describing the uncertainty.

[0029] According to interval mathematics theory, the uncertainty parameter can be expressed as an interval variable, as shown below: (9); in, For an interval vector of uncertain mechanical parameters; and These are the corresponding lower and upper bounds, respectively; It is the first vector i One component; and These are the lower and upper bounds, respectively; m is the number of uncertain mechanical parameters.

[0030] According to interval mathematics theory, equation (9) can be rewritten in the form of center value and radius, as shown below: (10); (11); in, For the nominal value of the interval, The radius of the interval; For interval variables of uncertain mechanical parameters, it is the complete interval expression of uncertain mechanical parameters; It is the first i The nominal values ​​of an uncertain mechanical parameter component within an interval; For the first i The radius of the interval of an uncertain mechanical parameter component.

[0031] Considering the incoming flow velocity as an uncertain parameter, then we have: (12); Therefore, the non-probabilistic interval method can be used to quantify the uncertain incoming flow parameters into interval variables.

[0032] Step S2: Based on Bayesian theory, new sample points are introduced to update the interval parameters, establishing a connection between the non-probability quantization set and the credibility.

[0033] In traditional non-probabilistic interval models, parameter uncertainty is typically represented as a fixed interval. This lacks a mechanism for updating cognition based on new evidence and makes it impossible to quantify the reliability of predictions. Here, we introduce a Bayesian non-probabilistic mixture framework. Its core idea is to treat the parameters in the non-probabilistic interval model (e.g., interval radius and midpoint) as random variables and assign them a prior distribution based on experience or preliminary judgment. Based on Bayesian theory, the prior distribution is updated by introducing new experimental or observational sample data, thus obtaining a posterior distribution reflecting the latest cognitive state. The mathematical core of this process is deriving the posterior probability density function of the interval parameters.

[0034] According to Bayesian theory, the posterior probability density of the interval parameter is as follows: (13); in, This represents the posterior probability density. This represents the prior probability density. The sampling density of the sample; Let be a normalization constant, representing the marginal density of the sample.

[0035] Using the average distribution as the prior distribution for the interval radius, the probability density function of the uniform distribution is as follows: (14); in, , These are the upper and lower boundaries.

[0036] The interval method assumes that all samples are equally likely to be distributed in the interval. Samples are drawn from a uniform distribution, and the sampling density is as follows: (15); in, These are the unknown parameters of the target to be estimated in Bayesian inference.

[0037] From this, we can derive the expression for the posterior probability density, as shown below: (16); in, The independent sample size inferred from the Bayesian parameters.

[0038] Given credibility Integrating over the posterior distribution, as shown below: (17); Finally, the numerical solution for the interval parameters under a given confidence level is obtained, as shown below: (18); in, To achieve a given level of confidence The Bayesian confidence upper bound of the interval radius of the uncertain mechanical parameters obtained by solving through the Bayesian posterior distribution is given.

[0039] Step S3: Using the buckling stability criterion as the failure criterion, conduct failure analysis of the underwater robotic arm's link structure to obtain the load multiplier and critical buckling load, and construct the limit state equation.

[0040] This invention employs a buckling stability criterion that distinguishes failure modes for refined static strength analysis of composite material structures.

[0041] For the buckling failure mode of the member, the buckling stability criterion is as follows: (19); in, This is referred to as the critical load, and in this invention, it is used as the ultimate buckling load. The elastic modulus of the material; The moment of inertia of the circular cross-section of the rod structure; For a considerable length; coefficient It is called the length factor, which characterizes the influence of the support method on the critical load.

[0042] In finite element analysis, the surface pressure of the member obtained by CFD calculation in flow fields with different incoming velocities is used as the prestress for subsequent buckling analysis. Under the constraint condition that one end of the member is fixed and the other end is free, the load multiplier can be obtained by applying a pressure load. .

[0043] Failure coefficient for constructing buckling criteria As shown below: (20); Construct the limit state equations when At that time, it is considered that the applied load did not reach the buckling load of the member, and the structure is safe. When the applied load exceeds the critical instability load, the structure is considered to buckle and become unstable.

[0044] Step S4: Use the Taylor series expansion method to perform uncertainty propagation analysis and solve for the failure coefficient response interval under buckling failure.

[0045] Let the response function of the structure be: (twenty one); Among them, the response function The equation of state is the buckling stability criterion.

[0046] Given that the uncertainty level of the parameters is usually small, and the response function is a monotonic function of the uncertain parameters, a first-order Taylor expansion can be performed on the response function to obtain the interval of the structural response function. This expansion uses information from the nominal value points and / or endpoints of the interval containing the uncertain parameters to evaluate the response limit of the response function over the entire interval, as shown below: (twenty two); in, These are the upper and lower bounds of the interval for the response function, respectively. The nominal value of the interval point response function; The first derivative of the response function with respect to each uncertainty variable can be obtained by combining composite material mechanics and finite element analysis methods.

[0047] Step S5: Combining stress intensity interference theory, compare the response interval with the limit state equation to establish a nonprobabilistic Bayesian reliable analysis model.

[0048] Based on the interval stress-strength interference model, the reliability of the failure coefficient for structural buckling instability is obtained as follows: response range [ , After that, it is compared with the critical value of the failure coefficient (equal to 0) to obtain the confidence level. Structural failure probability As shown below: (twenty three); Credibility level: The structural reliability is: (twenty four); in, For credibility Structural failure probability under certain conditions; For credibility The lower bound of the failure coefficient response range for buckling instability of an underwater robotic arm structure under certain conditions; For credibility The upper bound of the failure coefficient response range for buckling instability of an underwater robotic arm structure under certain conditions; For credibility Nonprobabilistic reliability of underwater robotic arm structures considering fluid-structure interaction effects under certain conditions.

[0049] Example 2 To better understand the features of this invention and its applicability to engineering practice, this embodiment first establishes the prestress field of the bar structure considering the incoming flow velocity. Samples are obtained by random sampling, and reliable interval parameters are calculated based on Bayesian theory. Uncertainty propagation analysis is performed using the Taylor series expansion method, and the limit state equation is constructed according to the buckling stability criterion to obtain the ultimate buckling load. Thus, the reliability of the structure not buckling failure under compressive load is calculated.

[0050] The geometric parameters of the member are: the member cross-section has a radius of 60mm, and the member length is 1000mm. Figure 2 As shown. The member material is structural steel, and its Young's modulus is... Poisson's ratio is 0.3, and bulk modulus is The shear modulus is The compressive yield strength is The rod itself is pre-applied with a pressure field generated by the water flow, a hydrostatic pressure load is applied to the rod, a fixed support is applied to one end of the rod, and a pressure load is applied to the other end.

[0051] The interval center is considered fixed, and the interval radius is considered an uncertain parameter to be updated. A new sample point is introduced to update the interval radius based on a non-probabilistic Bayesian reliable model update method. The proposed method uses a uniform distribution as the prior distribution of the parameter to be updated. Given a certain confidence level, and assuming a uniform prior distribution, the posterior distribution and posterior interval of the updated stiffness parameter interval radius are as follows: Figure 3 As shown.

[0052] Figure 4 This study demonstrates the variation of the radius of the uncertainty interval for updated physical parameters as the confidence level increases when the prior distribution is uniform: to ensure a higher confidence level, the radius of the uncertainty interval increases accordingly. This pattern is highly consistent with common understanding in engineering practice.

[0053] By employing a Bayesian update mechanism, the wide range of estimations resulting from high reliability requirements can be effectively narrowed while accurately quantifying uncertainty. Under the premise of achieving the same level of reliability, this invention provides a more compact and accurate uncertainty range than traditional methods, thereby significantly reducing the conservatism of the design and finding a better balance between ensuring safety and achieving goals such as economy, lightweight design, and high performance.

[0054] Uncertainty propagation analysis was performed using the Taylor series expansion method, combined with finite element analysis. By changing the uncertain physical parameters, the first derivative of the Taylor series expansion was obtained, leading to the response boundary of the buckling failure coefficient of the member. Stress intensity interference theory was applied to calculate the structural reliability under different confidence levels. The results are as follows: Figure 5 As shown, the computational reliability of the structure decreases as the required confidence level of the evaluation results increases. This negative correlation, consistent with theoretical expectations, indicates that at higher confidence levels, a wider range of uncertainty parameters must be considered to obtain more conservative reliability values.

[0055] Therefore, this invention employs the aforementioned non-probabilistic reliability analysis method for underwater manipulators considering fluid-structure interaction effects. It establishes a reliability analysis model with credibility for interval uncertainty quantification of underwater manipulator link structures under fluid-structure interaction, considering multi-source uncertainties. Addressing the problem of inaccurate reliability assessment due to insufficient input variable sample information, based on Bayesian theory and interval models, the interval radius is considered to be an uncertain parameter of a prior distribution following a uniform distribution. The relationship between the interval radius and the credibility level is obtained through theoretical solutions. Taylor series expansion is used, combined with buckling stability criteria, to calculate the structural credibility and reliability. Simulation results show that the proposed non-probabilistic Bayesian model with a prior uniform distribution can better handle the balance between conservatism and credibility of the interval model. With the introduction of new sample points, the reliability will continuously improve, providing greater design space for the design of underwater manipulator link structures considering the influence of incoming flow velocity.

[0056] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A nonprobabilistic reliability analysis method for an underwater robotic arm considering fluid-structure interaction effects, characterized in that, Includes the following steps: Step S1: Derive the dynamic response relationship of the underwater robotic arm link structure under fluid-structure interaction, and use the non-probabilistic interval method to quantify the uncertainty of fluid load parameters under finite sample conditions; Step S2: Based on Bayesian theory, it is assumed that the interval parameter is an uncertain parameter that follows a uniform distribution. Sample points are introduced for updating, and the relationship between the interval parameter and the confidence level is obtained through analytical solution. Step S3: Considering the failure mode of the member under compression, the buckling stability criterion is used as the failure criterion to carry out the structural strength and stability analysis of the underwater robotic arm member and obtain the critical buckling load. Step S4: Use the Taylor series expansion method to perform uncertainty propagation analysis and solve for the structural response interval corresponding to the non-probability interval of the input uncertainty parameter; Step S5: Combining stress-intensity interference theory or tolerance interference theory, compare the response interval with the limit state equation to establish a nonprobabilistic Bayesian reliable analysis model.

2. The non-probabilistic reliability analysis method for an underwater robotic arm considering fluid-structure interaction effects according to claim 1, characterized in that, In step S1, the stream function and velocity potential of the flow around the cylinder are solved according to the potential flow theory, as shown below: （1）； Applying Bernoulli's equation, we have: （2）； pressure coefficient The expression is: （3）； The final pressure coefficient can be obtained by combining formulas (1)-(3). The expression is as follows: （4）； in, The tangential velocity of the cylindrical surface; The incoming flow velocity; For incoming static pressure; For fluid density; Surface pressure; Pressure coefficient; angle The calculation starts from the point directly opposite the incoming flow.

3. The non-probabilistic reliability analysis method for an underwater robotic arm considering fluid-structure interaction effects according to claim 2, characterized in that, In step S1, consider a load under arbitrary lateral load. and axial force For members under combined action, take a small segment. Analysis is performed, and the torque balance equation for the rear end point of the micro-segment is as follows: （5）； in, The bending moment is the bending moment at the left cross-section of the micro-segment; This is the differential increment of the bending moment; The shear force is the force on the left side of the micro-segment. This represents the differential increment of the shear force; For any lateral distributed load acting on the member; This refers to the constant axial pressure acting on the end of the member; Let x be the lateral deflection of the member perpendicular to its axis at coordinate x; The lateral deflection of the right side of the micro-segment perpendicular to the axis of the member; After simplification, it is considered The torque balance equations after the effect are as follows: （6）； in, This represents the differential increment of the deflection; By introducing the constitutive relations of the material and the moment-curvature equation of the beam, we further obtain: （7）； in, The Young's modulus of the rod material; Let be the moment of inertia of the cross section of the rod about the neutral axis; Introducing amplification factor As shown below: （8）； in, This is the theoretical limit load.

4. The non-probabilistic reliability analysis method for an underwater robotic arm considering fluid-structure interaction effects according to claim 3, characterized in that, In step S1, the uncertainty is described using a non-probabilistic interval mathematics method. According to interval mathematics theory, the uncertainty parameter is expressed as an interval variable, as shown below: （9）； in, For an interval vector of uncertain mechanical parameters; and These are the corresponding lower and upper bounds, respectively; It is the i-th component of the vector; and These are the lower and upper bounds, respectively; m is the number of uncertain mechanical parameters; According to interval mathematics theory, equation (9) can be rewritten in the form of center value and radius, as shown below: （10）； （11）； in, For the nominal value of the interval, The radius of the interval; For interval variables of uncertain mechanical parameters, it is the complete interval expression of uncertain mechanical parameters; For the first i The nominal values ​​of an uncertain mechanical parameter component within an interval; For the first i The radius of the interval of an uncertain mechanical parameter component; Considering the incoming flow velocity as an uncertain parameter, then we have: （12）； Therefore, the uncertain incoming flow parameters are quantified into interval variables using the non-probabilistic interval method.

5. The non-probabilistic reliability analysis method for an underwater robotic arm considering fluid-structure interaction effects according to claim 4, characterized in that, In step S2, according to Bayesian theory, the posterior probability density of the interval parameters is as follows: （13）； in, This represents the posterior probability density. This represents the prior probability density. The sampling density of the sample; Let be a normalization constant, representing the marginal density of the sample; Using the average distribution as the prior distribution for the interval radius, the probability density function of the uniform distribution is as follows: （14）； in, , For upper and lower boundaries; The interval method assumes that all samples are equally likely to be distributed in the interval. Samples are drawn from a uniform distribution, and the sampling density is as follows: （15）； in, These are the unknown parameters of the target to be estimated in Bayesian inference. From this, we can derive the expression for the posterior probability density, as shown below: （16）； in, The independent sample size inferred from the Bayesian parameters; Given credibility Integrating over the posterior distribution, as shown below: （17）； Finally, the numerical solution for the interval parameters under a given confidence level is obtained, as shown below: （18）； in, To achieve a given level of confidence Under the given conditions, the Bayesian confidence upper bound of the interval radius of the uncertain mechanical parameters obtained by solving through the Bayesian posterior distribution.

6. The non-probabilistic reliability analysis method for an underwater robotic arm considering fluid-structure interaction effects according to claim 5, characterized in that, In step S3, the buckling stability criterion that distinguishes failure modes is used to perform static strength analysis of the composite structure. For the buckling failure mode of the member, the buckling stability criterion is as follows: （19）； in, This is referred to as the critical load, and in this invention, it is used as the ultimate buckling load. The elastic modulus of the material; The moment of inertia of the circular cross-section of the rod structure; For a considerable length; coefficient This is called the length factor, which characterizes the influence of the support method on the critical load. In finite element analysis, the surface pressure of the member obtained by CFD calculation in flow fields with different incoming velocities is used as the prestress for subsequent buckling analysis. Under the constraint condition that one end of the member is fixed and the other end is free, the load multiplier can be obtained by applying a pressure load. ; Failure coefficient for constructing buckling criteria As shown below: （20）； Construct the limit state equations when When the applied load does not reach the buckling load of the member, the structure is considered safe; when When the applied load exceeds the critical instability load, the structure is determined to buckle and become unstable.

7. The non-probabilistic reliability analysis method for an underwater robotic arm considering fluid-structure interaction effects according to claim 6, characterized in that, In step S4, uncertainty propagation analysis is performed using the Taylor series expansion method to solve for the failure coefficient response interval under buckling failure conditions. The specific process is as follows: Let the response function of the structure be: （21）； Among them, the response function The state equation is the buckling stability criterion. A first-order Taylor expansion of the response function is performed, and the response bound of the response function over the entire interval is evaluated using information from the nominal value points and / or the endpoints of the interval containing the uncertainty parameter, as shown below: （22）； in, These are the upper and lower bounds of the interval for the response function, respectively. The nominal value of the interval point response function; This is the first derivative of the response function with respect to each uncertainty variable.

8. The non-probabilistic reliability analysis method for an underwater robotic arm considering fluid-structure interaction effects according to claim 7, characterized in that, In step S5, the response interval is compared with the limit state equation by combining the stress intensity interference theory, and a non-probabilistic Bayesian reliable analysis model is established. The specific process is as follows: Based on the interval stress-strength interference model, the reliability of the failure coefficient for structural buckling instability is obtained as follows: response range [ , Afterwards, it was compared with the critical value of the failure coefficient to obtain a confidence level of [value missing]. Structural failure probability As shown below: （23）； The credibility is then The structural reliability is: （24）； in, For credibility Structural failure probability under certain conditions; For credibility The lower bound of the failure coefficient response range for buckling instability of an underwater robotic arm structure under certain conditions; For credibility The upper bound of the failure coefficient response range for buckling instability of an underwater robotic arm structure under certain conditions; For credibility Nonprobabilistic reliability of underwater robotic arm structures considering fluid-structure interaction under certain conditions.

Images