Method for evaluating multi-stage degradation related competing failures of underwater pressure hull

Abstract

The application discloses a method for evaluating multi-stage degradation related competing failure of underwater pressure hulls, and belongs to the technical field of reliability evaluation of underwater equipment, which is used for reliability evaluation of underwater equipment and comprises the following steps: calculating the overall degradation rate based on degradation quantity, and calculating the posterior membership probability and the effective estimation value of stage parameters; constructing the inter-stage correlation function and the multi-stage dynamic coupling model by using the statistical characteristics of the average degradation rate of each stage, so that the overall degradation statistical expectation is obtained; introducing the inter-stage correlation function after impact correction, so that the statistical expectation of the overall degradation process of the underwater pressure hull is corrected; calculating the system expected life based on the system overall competing failure reliability function, and evaluating the influence of the impact event and the degradation rate on the reliability. The competing failure reliability model considering the degradation and the impact simultaneously is established, so that the problem that the existing technology is difficult to accurately evaluate the reliability of the underwater pressure hull under the condition of multi-stage degradation and impact coupling is solved.

Description

Technical Field

[0001] This invention discloses a method for assessing multi-stage degradation-related competitive failures of underwater pressure tanks, belonging to the field of underwater equipment reliability assessment technology. Background Technology

[0002] As a crucial load-bearing and protective structure for deep-sea equipment, the performance of underwater pressure tanks directly impacts the stability and reliability of the entire platform. During long-term service, pressure tanks are subjected to a combination of factors, including high pressure, temperature gradients, cyclic loads, and ocean current impacts, leading to gradual degradation of material and structural properties. This degradation process exhibits significant staged and dynamic evolutionary characteristics, typically categorized into different phases: degradation initiation, stable development, and accelerated deterioration. Each phase corresponds to a different dominant damage mechanism and degradation rate, such as early-stage interfacial microcrack propagation, mid-stage structural fatigue accumulation, and late-stage plastic failure and leakage risk.

[0003] As service time increases, the degradation behavior of pressure tanks exhibits strong nonlinearity and uncertainty. Environmental disturbances and load fluctuations mean that the transitions between degradation stages are not fixed moments, but rather dynamic changes that occur with the evolution of the system state. Furthermore, statistical correlations often exist between degradation stages; the accumulation of damage in the previous stage has a continuous impact on the degradation rate and evolution path of subsequent stages, thus giving the degradation process temporal memory and coupling. In the complex environment of the deep sea, random impact loads (such as underwater oscillations, mechanical vibrations, or external collisions) can cause sudden stress disturbances to the pressure tank structure. The response to impacts differs significantly at different degradation stages; early impacts may only cause micro-damage, while later stages may lead to sudden structural failure. This competitive relationship between gradual degradation and sudden failure makes traditional single-stage or single-mode reliability assessment methods unable to accurately reflect the failure characteristics of pressure tanks in actual service.

[0004] Therefore, it is urgent to study the multi-stage degradation law of underwater pressure tanks, characterize the dynamic correlation between stages, and establish a competitive failure reliability model that simultaneously considers degradation and impact effects. This is of great engineering significance for improving the accuracy and reliability of underwater pressure tank structural safety assessment. Summary of the Invention

[0005] The purpose of this invention is to provide a multi-stage degradation-related competitive failure assessment method for underwater pressure tanks, in order to solve the problems in the prior art that make it difficult to accurately identify the degradation stages of underwater pressure tanks, quantify the uncertainty of stage boundaries, describe the degradation correlation between stages, and consider the impact of impact on failure.

[0006] A multi-stage degradation-related competing failure assessment method for underwater pressure tanks, including:

[0007] S1. Define the degradation amount of the underwater pressure tank, and calculate the overall degradation rate of the underwater pressure tank based on the degradation amount;

[0008] S2. Represent the degradation process as a piecewise parameterized model, combine the indicator function to calculate the posterior membership probability of each stage, and calculate the effective estimate of the stage parameters based on the posterior membership probability.

[0009] S3. Calculate the average degradation rate based on the degradation amount of the underwater pressure tank at different stages, calculate the correlation function of degradation rate between stages based on the expectation and variance of the average degradation rate, establish a dynamic coupling model of multi-stage degradation rate, and construct the statistical expectation of the overall degradation process of the underwater pressure tank.

[0010] S4. An impact effect correction term is introduced into the dynamic coupling model of stage degradation rate, and an inter-stage correlation function after impact correction is introduced to correct the statistical expectation of the overall degradation process of the underwater pressure tank.

[0011] S5. Reconstruct the degradation of the underwater pressure tank into a form that evolves over time, calculate the failure time, derive the degradation failure reliability function based on the failure time, set the bearing threshold to calculate the cumulative failure probability of sudden failure, and calculate the corresponding sudden failure reliability function. Define the total failure time, calculate the overall system competitive failure reliability function, and calculate the system expected lifetime, impact rate sensitivity function, and degradation rate sensitivity function based on the overall system competitive failure reliability function. Use the degradation failure reliability function, sudden failure reliability function, overall system competitive failure reliability function, expected lifetime, impact rate sensitivity function, and degradation rate sensitivity function as the evaluation results.

[0012] S1 includes, S1.1, defining the underwater pressure chamber at a given time. The amount of degradation is and calculate degradation rate :

[0013] ;

[0014] ;

[0015] In the formula, As a comprehensive impact factor, As a comprehensive influencing factor related to stress, As a comprehensive influencing factor related to temperature, As a comprehensive influencing factor related to material properties, It is a nonlinear degenerate function. Noise term;

[0016] S1 includes S1.2, defining the degradation acceleration. :

[0017] ;

[0018] Will Consider them as stage-specific change points, and let the number of stage-specific change points be . The degradation process of underwater pressure tanks is divided into stages based on the changing points. The overall degradation rate at any given time is:

[0019] ;

[0020] In the formula, As the first index, , for Time-phase degradation rate parameter for The dynamic modulation parameters of degradation rate by the time-dependent environmental driving factors. for Membership function at time stage.

[0021] S2 includes, S2.1, assuming the underwater pressure chamber degradation observation sequence during operation is... , In the interval Continuous change, This represents the total number of degradation observation points. The index number of the observation sequence, For the first The time corresponding to each degradation measurement Assuming two unknown variable points exist as the total duration of pressure chamber degradation monitoring. and ,satisfy Set minimum interval constraints , and satisfy The degradation process is represented as a piecewise parameterized model. :

[0022] ;

[0023] In the formula, , For the first The parameterized degradation function of the stage, For the first Stage parameter vector, For the observed noise term;

[0024] S2 includes S2.2, and the definition. Belongs to stage Posterior membership probability:

[0025] stage ;

[0026] In the formula, , , For probability, For indicator functions, For all observed degradation data;

[0027] Define the effective estimates of the phase parameters :

[0028] ;

[0029] In the formula, for The posterior expected value.

[0030] S3 includes S3.1, where the three stages of the underwater pressure tank degradation process correspond to different time intervals. , and , define the first Average degradation rate of the stage for:

[0031] ;

[0032] In the formula, , ;

[0033] Expected average degradation rate during the definition phase With variance They are respectively:

[0034] ;

[0035] ;

[0036] In the formula, The integral symbol is used. It is a joint prior distribution;

[0037] Introducing the inter-stage degradation rate correlation function :

[0038] ;

[0039] In the formula, For the second index, For the first Average degradation rate of the stage For the stage and stage The average degradation rate covariance between them Let Variance be the variance.

[0040] S3 includes, S3.2, establishing a dynamic coupling model for multi-stage degradation rates:

[0041] ;

[0042] In the formula, For the stage steady-state degradation rate, , For the stage steady-state degradation rate, For the stage The zero-mean random disturbance term, For the stage The inter-stage coupling coefficient, , For the stage The random disturbance term within the period follows a certain order. , It follows a normal distribution;

[0043] Statistical expectation of the overall degradation process of underwater pressure tanks for:

[0044] ;

[0045] In the formula, Contribution to average degradation at each stage This represents the coupling increment of inter-stage correlation.

[0046] S4 includes, S4.1, assuming the system is subjected to degradation during the degradation process. A random shock event, the time of each shock occurrence is denoted as . , For the impact event index, the impact amplitude is Follows intensity distribution An impact effect correction term is introduced into the dynamic coupling model of stage degradation rate:

[0047] ;

[0048] ;

[0049] In the formula, The term represents the instantaneous degradation rate increment caused by the impact. For the instantaneous impact;

[0050] Calculate the impact-corrected inter-stage correlation function :

[0051] ;

[0052] ;

[0053] In the formula, Degeneration stage Impact sensitivity coefficient, For the stage Degradation response weights, This represents the expected impact damage.

[0054] S4 includes S4.2. Ignoring the impact, the conditional mean propagation relationship between adjacent degradation stages is as follows:

[0055] ;

[0056] ;

[0057] In the formula, For the stage and stage The conditional mean propagation coefficient between them For the first The mean of the stage degradation rate, , For the first The mean of the stage degradation rate, ;

[0058] The corrected conditional mean propagation equation is:

[0059] ;

[0060] ;

[0061] In the formula, This is the impact coupling amplification factor. For the first The expected rate of degradation caused by the impact per unit time in a given stage;

[0062] Statistical expectation of the overall degradation process of the modified underwater pressure tank for:

[0063] .

[0064] S5 includes, S5.1, and will Evolution over time is represented as:

[0065] ;

[0066] In the formula, The instantaneous degradation rate after stage coupling. This represents the initial degenerate state of the system. For the integral variable corresponding to the time;

[0067] when Reaching the failure threshold When the system experiences degradation failure, the failure time is... for:

[0068] ;

[0069] In the formula, The infimum;

[0070] If the staged degradation process follows a Gaussian evolution law, derive the degradation failure reliability function of the staged degradation process. :

[0071] ;

[0072] In the formula, Let be the distribution function of degradation failure time. For the degradation process The mean, , For the degradation process standard deviation This is the cumulative distribution function of the standard normal distribution.

[0073] S5 includes, S5.2, which assumes the number of random shock events the system experiences during the degradation process. Impact arrival rate The impact amplitude of each impact is Follows intensity distribution When the impact amplitude exceeds the transient load-bearing threshold of the structure At that time, the system immediately failed, causing , To mitigate the sensitivity of the load-bearing capacity reduction coefficient, The inherent load-bearing threshold of the system in its initial, undegraded state; sudden failure within the time interval. Cumulative failure probability within for:

[0074] ;

[0075] Corresponding sudden failure reliability function for:

[0076] ;

[0077] The total failure time is defined as:

[0078] ;

[0079] In the formula, For sudden failure time;

[0080] System overall competition failure reliability function for:

[0081] .

[0082] S5 includes S5.3, based on Calculate life expectancy :

[0083] ;

[0084] Introducing reliability into impact arrival rate Stage degradation rate parameter The sensitivity function is used to evaluate the impact of shock events and degradation rates on reliability:

[0085] ;

[0086] ;

[0087] In the formula, Let be the impact rate sensitivity function. The degradation rate sensitivity function The sign of the partial derivative;

[0088] Ultimately , , , , and As an evaluation result.

[0089] Compared with the prior art, the present invention has the following beneficial effects: The present invention constructs a dynamic evolution equation for the degradation state of the pressure tank, combines the degradation acceleration variation law to realize the dynamic division of degradation stages, and uses a Bayesian variable point identification model to characterize the uncertainty of the stage boundary, obtains the stage membership probability at each moment, realizes adaptive identification of stage turning points in the degradation process, avoids the misjudgment of complex degradation processes by the traditional fixed threshold division method, realizes the dynamic and probabilistic division of degradation stages, thereby improving the accuracy and robustness of underwater pressure tank degradation feature identification in non-stationary environments;

[0090] By constructing a degradation rate correlation function and a dynamic coupling model of multi-stage degradation rates, a conditional covariance propagation mechanism is introduced to reveal the transmission relationship of degradation rates between stages. Furthermore, an impact response term is introduced to establish a modified model under the influence of impact, comprehensively describing the dynamic amplification effect of impact on degradation rates and stage correlations. Based on this, a competing failure model of degradation failure and sudden failure is constructed, which can simultaneously characterize the gradual degradation and sudden failure processes caused by random impacts, achieving unified modeling and reliability assessment of the multi-stage failure mechanism of underwater pressure tanks. Attached Figure Description

[0091] Figure 1 This is a flowchart of the method of the present invention;

[0092] Figure 2 This is a diagram illustrating the degradation process of an underwater pressure tank under the influence of the correlation between different degradation stages.

[0093] Figure 3 This is a simulation diagram of the degradation data of the underwater pressure tank;

[0094] Figure 4 This is a comparison chart of the reliability analysis results of the simulated data. Detailed Implementation

[0095] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention are described clearly and completely below. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0096] A multi-stage degradation-related competing failure assessment method for underwater pressure tanks, including:

[0097] S1. Define the degradation amount of the underwater pressure tank, and calculate the overall degradation rate of the underwater pressure tank based on the degradation amount;

[0098] S2. Represent the degradation process as a piecewise parameterized model, combine the indicator function to calculate the posterior membership probability of each stage, and calculate the effective estimate of the stage parameters based on the posterior membership probability.

[0099] S3. Calculate the average degradation rate based on the degradation amount of the underwater pressure tank at different stages, calculate the correlation function of degradation rate between stages based on the expectation and variance of the average degradation rate, establish a dynamic coupling model of multi-stage degradation rate, and construct the statistical expectation of the overall degradation process of the underwater pressure tank.

[0100] S4. An impact effect correction term is introduced into the dynamic coupling model of stage degradation rate, and an inter-stage correlation function after impact correction is introduced to correct the statistical expectation of the overall degradation process of the underwater pressure tank.

[0101] S5. Reconstruct the degradation of the underwater pressure tank into a form that evolves over time, calculate the failure time, derive the degradation failure reliability function based on the failure time, set the bearing threshold to calculate the cumulative failure probability of sudden failure, and calculate the corresponding sudden failure reliability function. Define the total failure time, calculate the overall system competitive failure reliability function, and calculate the system expected lifetime, impact rate sensitivity function, and degradation rate sensitivity function based on the overall system competitive failure reliability function. Use the degradation failure reliability function, sudden failure reliability function, overall system competitive failure reliability function, expected lifetime, impact rate sensitivity function, and degradation rate sensitivity function as the evaluation results.

[0102] S1 includes, S1.1, defining the underwater pressure chamber at a given time. The amount of degradation is and calculate degradation rate :

[0103] ;

[0104] ;

[0105] In the formula, As a comprehensive impact factor, As a comprehensive influencing factor related to stress, As a comprehensive influencing factor related to temperature, As a comprehensive influencing factor related to material properties, It is a nonlinear degenerate function. Noise term;

[0106] S1 includes S1.2, defining the degradation acceleration. :

[0107] ;

[0108] Will Consider them as stage-specific change points, and let the number of stage-specific change points be . The degradation process of underwater pressure tanks is divided into stages based on the changing points. The overall degradation rate at any given time is:

[0109] ;

[0110] In the formula, As the first index, , for Time-phase degradation rate parameter for The dynamic modulation parameters of degradation rate by the time-dependent environmental driving factors. for Membership function at time stage.

[0111] S2 includes, S2.1, assuming the underwater pressure chamber degradation observation sequence during operation is... , In the interval Continuous change, This represents the total number of degradation observation points. The index number of the observation sequence, For the first The time corresponding to each degradation measurement Assuming two unknown variable points exist as the total duration of pressure chamber degradation monitoring. and ,satisfy Set minimum interval constraints , and satisfy The degradation process is represented as a piecewise parameterized model. :

[0112] ;

[0113] In the formula, , For the first The parameterized degradation function of the stage, For the first Stage parameter vector, For the observed noise term;

[0114] S2 includes S2.2, and the definition. Belongs to stage Posterior membership probability:

[0115] stage ;

[0116] In the formula, , , For probability, For indicator functions, For all observed degradation data;

[0117] Define the effective estimates of the phase parameters :

[0118] ;

[0119] In the formula, for The posterior expected value.

[0120] S3 includes S3.1, where the three stages of the underwater pressure tank degradation process correspond to different time intervals. , and , define the first Average degradation rate of the stage for:

[0121] ;

[0122] In the formula, , ;

[0123] Expected average degradation rate during the definition phase With variance They are respectively:

[0124] ;

[0125] ;

[0126] In the formula, The integral symbol is used. It is a joint prior distribution;

[0127] Introducing the inter-stage degradation rate correlation function :

[0128] ;

[0129] In the formula, For the second index, For the first Average degradation rate of the stage For the stage and stage The average degradation rate covariance between them Let Variance be the variance.

[0130] S3 includes, S3.2, establishing a dynamic coupling model for multi-stage degradation rates:

[0131] ;

[0132] In the formula, For the stage steady-state degradation rate, , For the stage steady-state degradation rate, For the stage The zero-mean random disturbance term, For the stage The inter-stage coupling coefficient, , For the stage The random disturbance term within the period follows a certain order. , It follows a normal distribution;

[0133] Statistical expectation of the overall degradation process of underwater pressure tanks for:

[0134] ;

[0135] In the formula, Contribution to average degradation at each stage This represents the coupling increment of inter-stage correlation.

[0136] S4 includes, S4.1, assuming the system is subjected to degradation during the degradation process. A random shock event, the time of each shock occurrence is denoted as . , For the impact event index, the impact amplitude is Follows intensity distribution An impact effect correction term is introduced into the dynamic coupling model of stage degradation rate:

[0137] ;

[0138] ;

[0139] In the formula, The term represents the instantaneous degradation rate increment caused by the impact. For the instantaneous impact;

[0140] Calculate the impact-corrected inter-stage correlation function :

[0141] ;

[0142] ;

[0143] In the formula, Degeneration stage Impact sensitivity coefficient, For the stage Degradation response weights, This represents the expected impact damage.

[0144] S4 includes S4.2. Ignoring the impact, the conditional mean propagation relationship between adjacent degradation stages is as follows:

[0145] ;

[0146] ;

[0147] In the formula, For the stage and stage The conditional mean propagation coefficient between them For the first The mean of the stage degradation rate, , For the first The mean of the stage degradation rate, ;

[0148] The corrected conditional mean propagation equation is:

[0149] ;

[0150] ;

[0151] In the formula, This is the impact coupling amplification factor. For the first The expected rate of degradation caused by the impact per unit time in a given stage;

[0152] Statistical expectation of the overall degradation process of the modified underwater pressure tank for:

[0153] .

[0154] S5 includes, S5.1, and will Evolution over time is represented as:

[0155] ;

[0156] In the formula, The instantaneous degradation rate after stage coupling. This represents the initial degenerate state of the system. For the integral variable corresponding to the time;

[0157] when Reaching the failure threshold When the system experiences degradation failure, the failure time is... for:

[0158] ;

[0159] In the formula, The infimum;

[0160] If the staged degradation process follows a Gaussian evolution law, derive the degradation failure reliability function of the staged degradation process. :

[0161] ;

[0162] In the formula, Let be the distribution function of degradation failure time. For the degradation process The mean, , For the degradation process standard deviation This is the cumulative distribution function of the standard normal distribution.

[0163] S5 includes, S5.2, which assumes the number of random shock events the system experiences during the degradation process. Impact arrival rate The impact amplitude of each impact is Follows intensity distribution When the impact amplitude exceeds the transient load-bearing threshold of the structure At that time, the system immediately failed, causing , To mitigate the sensitivity of the load-bearing capacity reduction coefficient, The inherent load-bearing threshold of the system in its initial, undegraded state; sudden failure within the time interval. Cumulative failure probability within for:

[0164] ;

[0165] Corresponding sudden failure reliability function for:

[0166] ;

[0167] The total failure time is defined as:

[0168] ;

[0169] In the formula, For sudden failure time;

[0170] System overall competition failure reliability function for:

[0171] .

[0172] S5 includes S5.3, based on Calculate life expectancy :

[0173] ;

[0174] Introducing reliability into impact arrival rate Stage degradation rate parameter The sensitivity function is used to evaluate the impact of shock events and degradation rates on reliability:

[0175] ;

[0176] ;

[0177] In the formula, Let be the impact rate sensitivity function. The degradation rate sensitivity function The sign of the partial derivative;

[0178] Ultimately , , , , and As an evaluation result.

[0179] The larger the value, the more sensitive the system is to shocks. The degradation rate sensitivity function is used to evaluate the sensitivity of reliability to changes in degradation rate at each stage. The larger the value, the more sensitive the system is to the degradation rate at that stage.

[0180] The derivation process of the overall degradation rate of the underwater pressure tank includes the division of degradation stages based on the dynamic changes in degradation rate and degradation acceleration, and the definition of degradation acceleration. for Second derivative with respect to time:

[0181] ;

[0182] In the formula, The differential symbol;

[0183] When the degradation acceleration or amplitude changes significantly, it indicates a turning point in the degradation mechanism or rate characteristics, which can be regarded as a stage change point. For a typical three-stage degradation model, the system degradation process goes through three stages: early stage of latent degradation, middle stage of stable degradation, and late stage of accelerated degradation. This marks the turning point in the system's transition from the initial latent stage of degradation to the stable period. This is the turning point where the system transitions from a stable phase to an accelerated phase. As the first index, The three-stage degradation model satisfy:

[0184] ;

[0185] In the formula, The time position of the stage change point can be directly determined from the zero point of the degradation acceleration;

[0186] The degradation process is divided as follows:

[0187] ;

[0188] In the formula, This is the early, latent stage of degradation. This is the stable phase of the intermediate stage of degradation. This is the accelerated stage of late-stage degradation.

[0189] set up To ensure the physical rationality of the stage division, the continuity condition of the degenerate state quantities should be satisfied at the stage boundary as a stage transition point.

[0190] ;

[0191] In the formula, , Let i be the end time of stage i, and let l be the left-hand limit time. Let i be the end time of stage i, and let the right-hand limit time be... In the stage Degenerate state quantities near the end of the time interval Let i+1 be the degenerate state quantity at the very beginning of stage i+1;

[0192] Each stage This can be expressed in parameterized form as follows:

[0193] ;

[0194] In the formula, For the first Each stage ;

[0195] To avoid abrupt changes or discontinuities in the division between degradation stages, an introduction is made. :

[0196] ;

[0197] ;

[0198] The overall degradation rate of the underwater pressure tank was obtained as follows:

[0199] ;

[0200] To facilitate engineering implementation, an instantaneous degradation rate change index is defined. ,when The appearance of a significant peak indicates a clear reversal in the trend of degradation rate change. This moment corresponds to a high-probability region of degradation stage transition, and can provide candidate time intervals and prior constraints for degradation stage change points.

[0201] ;

[0202] In the formula, for The average value. When When a significant peak appears, it indicates a sudden change in the trend of degradation rate, which serves as a dynamic criterion for stage change points.

[0203] The process of calculating the effective estimates of stage membership probabilities and stage parameters at each time step using the Bayesian change point identification framework includes establishing... Afterwards, and Assign a joint prior distribution:

[0204] ;

[0205] Set to no less than the total observation time 10%;

[0206] Take the weak information prior of the normal distribution, and the noise variance. Negation prior information , Proportional to;

[0207] Given the changing point, the likelihood function of the observed data is:

[0208] ;

[0209] In the formula, Let be the likelihood function. For the first The time interval corresponding to the stage It is an exponential function;

[0210] According to Bayes' theorem, the joint posterior distribution is:

[0211] ;

[0212] In the formula, This is the set of parameter vectors for the three degradation stages. The prior distribution of the parameters for the three degradation stages is usually taken as a normal weak information prior.

[0213] This posterior distribution simultaneously reflects the uncertainty of the change point, the uncertainty of the degradation parameters at each stage, and the contribution of observation noise;

[0214] After obtaining the parameters and change points using Markov chain Monte Carlo sampling, the posterior sample set of the parameters and change points is then obtained. , The total number of samples, For sampling index, , For the s-th sample, the transition point from stage 1 to stage 2, For the first The transition points from stage 2 to stage 3 obtained from the sampling are used to obtain the posterior confidence intervals of the transition points based on the sample distribution:

[0215] ;

[0216] In the formula, For the sample -Quantities, The significance level is defined as (0, 1). For the stage change point of Posterior confidence intervals reflect the uncertainty at the turning point;

[0217] Final definition and .

[0218] The statistical expectation derivation process of the overall degradation process of the underwater pressure tank is as follows: Define the average degradation rate of each stage, calculate the expectation and variance of the average degradation rate of each stage, and introduce the correlation function of degradation rate between stages. This is used to describe the dependency between the degradation rates of adjacent degradation stages. At that time, an increase in the rate of degradation in the previous stage will accelerate the degradation in the next stage; when At this time, there is an inter-stage degradation inhibition effect. This correlation modeling provides a basis for the conditional mean propagation and reliability assessment of the subsequent degradation process, resulting in significant differences in reliability results when considering stage correlation versus ignoring stage correlation.

[0219] Considering the sequential nature of degradation evolution, a conditional covariance propagation model is constructed between stages. The conditional mean of the degradation rate in a later stage being influenced by the previous stage is expressed as:

[0220] ;

[0221] ;

[0222] In the formula, The degradation rate propagation coefficient, For the stage degradation rate The statistical expected value (mean). For the stage degradation rate The statistical expectation (mean);

[0223] A multi-stage degradation rate dynamic coupling model is established to comprehensively describe the stage evolution relationship of underwater pressure tank degradation, wherein if This indicates that adjacent stages are completely independent; if If the degradation rate of the next stage partially inherits the trend of the previous stage, this part can be used to compare the differences in system reliability when considering stage correlation and when not considering stage correlation.

[0224] The dynamic coupling model of degradation rates at each stage is embedded into a continuous description of the overall degradation process:

[0225] ;

[0226] ;

[0227] In the formula, For the first Instantaneous degradation rate after stage coupling;

[0228] Finally, the statistical expectation of the overall degradation process of the underwater pressure tank was obtained.

[0229] The derivation of the multi-stage degradation process of underwater pressure tanks under impact includes using the Poisson process to describe the arrival process of the impact event:

[0230] ;

[0231] ;

[0232] In the formula, The impact incidence rate per unit time. This refers to the cumulative impact intensity.

[0233] The instantaneous contribution of each impact event to the system degradation is characterized by the impact damage function:

[0234] ;

[0235] ;

[0236] In the formula, Let be the impact damage function. For the stage Impact resistance characteristic parameters are used to characterize the degradation stage. Sensitivity to shock; It is in the form of an exponential function. For the instantaneous damage caused by the impact event, here and For the stage The relevant constants reflect the differences in sensitivity to the same impact intensity at each stage;

[0237] Within this stochastic shock model framework, the expected value and variance of cumulative shock damage can be written as follows:

[0238] ;

[0239] ;

[0240] In the formula, Indicates the time of impact Index of the current stage of degradation;

[0241] Then, by introducing a correction term for the impact effect and integrating over time, the cumulative expression of the degradation can be obtained:

[0242] ;

[0243] In the formula, For degradation transitions caused by shocks, the value is non-zero only at the moment the shock occurs;

[0244] During the operation of underwater pressure tanks, external shocks not only directly affect the degradation rate but also alter the correlation between adjacent degradation stages. To characterize this effect, we introduce... When the system degenerates to a later stage, and An increase in the value indicates a higher sensitivity to shocks in later stages, thus strengthening the correlation between stages. Based on the modified correlation function, a modified conditional mean propagation equation can be defined to describe the conditional expectation of the degradation rate in the next stage given the degradation rate in the previous stage and the cumulative shock information. This equation considers the cumulative effect of the shock process and updates the stages accordingly. The probability distribution of degradation rate is obtained, and finally the statistical expectation of the overall degradation process of the underwater pressure tank is obtained.

[0245] The estimation process for degradation evolution parameters, shock statistics parameters, and failure threshold parameters includes:

[0246] Inference using maximum likelihood estimation , The likelihood function is:

[0247] ;

[0248] In the formula, ;

[0249] The optimal estimate is obtained by maximizing the log-likelihood function. :

[0250] ;

[0251] Incidence of shock events Impact intensity distribution Obtained from statistical analysis of event observation data; if the impact arrival process follows a homogeneous Poisson process, , In the time interval The total number of shock events actually observed within the country. This is an estimate of the average impact arrival rate; if the impact process is a non-homogeneous Poisson process, it is obtained through time-segmented statistics or kernel density estimation. The time-varying form of the impact amplitude and its distribution parameters can be obtained using the sample moment method; the degradation failure threshold and load-bearing threshold attenuation coefficient It is obtained by fitting the extreme value distribution of structural limit state tests or historical failure data.

[0252] like Figure 2 As shown, the degradation process of underwater pressure tanks exhibits multi-stage evolution characteristics over time, which can be divided into three stages: the initial latent stage of degradation, the middle stable stage of degradation, and the late accelerated stage of degradation, each represented by a degradation function. , and Description. The stage change point is... and Its posterior confidence interval Characterizing the uncertainty at the stage boundary. (Dashed arrow) This indicates the correlation and transmission relationship of degradation rates between stages, reflecting the influence of the degradation state of the previous stage on the degradation rate of the next stage; when the degradation trajectory crosses the degradation threshold... At that time, the system degraded and failed.

[0253] like Figure 3 As shown, the Monte Carlo method was used in the experiment to generate simulated degradation data of the underwater pressure tank. By setting different degradation rates and random disturbance levels in segments, a time series of degradation with three-stage characteristics was constructed to simulate the degradation evolution of the pressure tank during deep-sea service. Figure 3 As shown, in the early stage of degradation, the degradation growth is slow and the fluctuations are small, corresponding to the latent stage of degradation initiation; in the middle stage, the degradation rate remains relatively stable; in the late stage, the degradation rate increases significantly, and the degradation curve shows an accelerating upward trend, reflecting the accelerated degradation stage of rapid deterioration of structural performance.

[0254] like Figure 4As shown, based on simulated degradation data, the method proposed in this invention is applied to calculate the changes in system reliability considering and not considering the correlation between degradation stages. The reliability comparison results show that, considering the correlation between degradation stages, the cumulative effect of degradation in the previous stage will accelerate the degradation in the subsequent stage, thus causing the system reliability to decline more rapidly over time. However, when the correlation between stages is ignored, the reliability decreases relatively slowly, making it difficult to reflect the actual situation of accelerated degradation in the later stages. Comparative analysis verifies the effectiveness of the method of this invention in characterizing the coupling effect of multi-stage degradation.

[0255] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for assessing multi-stage degradation-related competing failures of underwater pressure tanks, characterized in that, include: S1. Define the degradation amount of the underwater pressure tank, and calculate the overall degradation rate of the underwater pressure tank based on the degradation amount; S2. Represent the degradation process as a piecewise parameterized model, combine the indicator function to calculate the posterior membership probability of each stage, and calculate the effective estimate of the stage parameters based on the posterior membership probability. S3. Calculate the average degradation rate based on the degradation amount of the underwater pressure tank at different stages, calculate the correlation function of degradation rate between stages based on the expectation and variance of the average degradation rate, establish a dynamic coupling model of multi-stage degradation rate, and construct the statistical expectation of the overall degradation process of the underwater pressure tank. S4. An impact effect correction term is introduced into the dynamic coupling model of stage degradation rate, and an inter-stage correlation function after impact correction is introduced to correct the statistical expectation of the overall degradation process of the underwater pressure tank. S5. Reconstruct the degradation of the underwater pressure tank into a form that evolves over time, calculate the failure time, derive the degradation failure reliability function based on the failure time, set the bearing threshold to calculate the cumulative failure probability of sudden failure, and calculate the corresponding sudden failure reliability function. Define the total failure time, calculate the overall competitive failure reliability function of the system, and calculate the expected life, impact rate sensitivity function, and degradation rate sensitivity function of the system based on the overall competitive failure reliability function of the system. Use the degradation failure reliability function, sudden failure reliability function, overall competitive failure reliability function of the system, expected life, impact rate sensitivity function, and degradation rate sensitivity function as the evaluation results. S1 includes, S1.1, defining the underwater pressure chamber at a given time. The amount of degradation is and calculate degradation rate : ； ； In the formula, As a comprehensive impact factor, As a comprehensive influencing factor related to stress, As a comprehensive influencing factor related to temperature, As a comprehensive influencing factor related to material properties, It is a nonlinear degenerate function. Noise term; S1 includes S1.2, defining the degradation acceleration. : ； Will Consider them as stage-specific change points, and let the number of stage-specific change points be . The degradation process of underwater pressure tanks is divided into stages based on the changing points. The overall degradation rate at any given time is: ； In the formula, As the first index, , for Time-phase degradation rate parameter for The dynamic modulation parameters of degradation rate by the time-dependent environmental driving factors. for Membership function at time stage.

2. The method for assessing multi-stage degradation-related competing failures of underwater pressure tanks according to claim 1, characterized in that, S2 includes, S2.1, assuming the underwater pressure chamber degradation observation sequence during operation is... , In the interval Continuous change, This represents the total number of degradation observation points. The index number of the observation sequence, For the first The time corresponding to each degradation measurement Assuming two unknown variable points exist as the total duration of pressure chamber degradation monitoring. and ,satisfy Set minimum interval constraints , and satisfy The degradation process is represented as a piecewise parameterized model. : ； In the formula, , For the first The parameterized degradation function of the stage, For the first Stage parameter vector, For the observed noise term; S2 includes S2.2, and the definition. Belongs to stage Posterior membership probability: stage ; In the formula, , , For probability, For indicator functions, For all observed degradation data; Define the effective estimates of the phase parameters : ； In the formula, for The posterior expected value.

3. The method for assessing multi-stage degradation-related competitive failures of underwater pressure tanks according to claim 2, characterized in that, S3 includes S3.1, where the three stages of the underwater pressure tank degradation process correspond to different time intervals. , and , define the first Average degradation rate of the stage for: ； In the formula, , ; Expected average degradation rate during the definition phase With variance They are respectively: ； ； In the formula, The integral symbol is used. It is a joint prior distribution; Introducing the inter-stage degradation rate correlation function : ； In the formula, For the second index, For the first Average degradation rate of the stage For the stage and stage The average degradation rate covariance between them Let Variance be the variance.

4. The method for assessing multi-stage degradation-related competitive failures of underwater pressure tanks according to claim 3, characterized in that, S3 includes, S3.2, establishing a dynamic coupling model for multi-stage degradation rates: ； In the formula, For the stage steady-state degradation rate, , For the stage steady-state degradation rate, For the stage The zero-mean random disturbance term, For the stage The inter-stage coupling coefficient, , For the stage The random disturbance term within the period follows a certain order. , It follows a normal distribution; Statistical expectation of the overall degradation process of underwater pressure tanks for: ； In the formula, Contribution to average degradation at each stage This represents the coupling increment of inter-stage correlation.

5. The method for assessing multi-stage degradation-related competitive failures of underwater pressure tanks according to claim 4, characterized in that, S4 includes, S4.1, assuming the system is subjected to degradation during the degradation process. A random shock event, the time of each shock occurrence is denoted as . , For the impact event index, the impact amplitude is Follows intensity distribution An impact effect correction term is introduced into the dynamic coupling model of stage degradation rate: ； ； In the formula, The term represents the instantaneous degradation rate increment caused by the impact. For the instantaneous impact; Calculate the impact-corrected inter-stage correlation function : ； ； In the formula, Degeneration stage Impact sensitivity coefficient, For the stage Degradation response weights, This represents the expected impact damage.

6. The method for assessing multi-stage degradation-related competitive failures of underwater pressure tanks according to claim 5, characterized in that, S4 includes S4.

2. Ignoring the impact, the conditional mean propagation relationship between adjacent degradation stages is as follows: ； ； In the formula, For the stage and stage The conditional mean propagation coefficient between them For the first The mean of the stage degradation rate, , For the first The mean of the stage degradation rate, ; The corrected conditional mean propagation equation is: ； ； In the formula, This is the impact coupling amplification factor. For the first The expected rate of degradation caused by the impact per unit time in a given stage; Statistical expectation of the overall degradation process of the modified underwater pressure tank for: 。 7. The method for assessing multi-stage degradation-related competing failures of underwater pressure tanks according to claim 6, characterized in that, S5 includes, S5.1, and will Evolution over time is represented as: ； In the formula, The instantaneous degradation rate after stage coupling. This represents the initial degenerate state of the system. For the integral variable corresponding to the time; when Reaching the failure threshold When the system experiences degradation failure, the failure time is... for: ； In the formula, The infimum; If the staged degradation process follows a Gaussian evolution law, derive the degradation failure reliability function of the staged degradation process. : ； In the formula, Let be the distribution function of degradation failure time. For the degradation process The mean, , For the degradation process standard deviation This is the cumulative distribution function of the standard normal distribution.

8. The method for assessing multi-stage degradation-related competing failures of underwater pressure tanks according to claim 7, characterized in that, S5 includes, S5.2, which assumes the number of random shock events the system experiences during the degradation process. Impact arrival rate The impact amplitude of each impact is Follows intensity distribution When the impact amplitude exceeds the transient load-bearing threshold of the structure At that time, the system immediately failed, causing , To mitigate the sensitivity of the load-bearing capacity reduction coefficient, The inherent load-bearing threshold of the system in its initial, undegraded state; sudden failure within the time interval. Cumulative failure probability within for: ； Corresponding sudden failure reliability function for: ； The total failure time is defined as: ； In the formula, For sudden failure time; System overall competition failure reliability function for: 。 9. The method for assessing multi-stage degradation-related competitive failures of underwater pressure tanks according to claim 8, characterized in that, S5 includes S5.3, based on Calculate life expectancy : ； Introducing reliability into impact arrival rate Stage degradation rate parameter The sensitivity function is used to evaluate the impact of shock events and degradation rates on reliability: ； ； In the formula, Let be the impact rate sensitivity function. The degradation rate sensitivity function The sign of the partial derivative; Ultimately , , , , and As an evaluation result.

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