Reliability Assessment Method of Marine Engine System under the Action of External Shocks

Abstract

The present invention relates to a reliability assessment method for a marine engine system under the action of external shocks, and relates to the technical field of reliability assessment. In view of the problem of inaccurate reliability assessment results of marine engine systems in the prior art, the present application fully considers the impact of external shocks on the performance degradation process of marine engine systems, and finds the intrinsic connection between external shocks and the performance degradation rate and sudden failure threshold changes of marine engine systems. When evaluating the reliability of marine engine systems, the sudden changes in degradation levels caused by multiple random shocks, the increase in degradation rate, and the reduction in failure threshold in the extreme shock model should be considered simultaneously to obtain more accurate reliability assessment results of marine engine systems and avoid overestimation of the reliability of marine engine systems.

Description

Technical Field

[0001] The present invention relates to the technical field of reliability assessment, and in particular to a reliability assessment method for a marine engine system under external impact. Background Art

[0002] After being put into operation, marine engine systems experience gradual performance degradation throughout their service life due to the influence of various factors. These factors can be broadly categorized as internal (such as wear, corrosion, fatigue, oxidation, and aging) and external, incidental (such as shock, stress, and load). The degradation process caused by internal factors is called the natural degradation process, while the degradation process caused by external factors is called the shock process. During this process, marine engine systems can fail due to performance degradation, known as degradation failure, or they can fail suddenly due to external shocks, known as sudden failure. Therefore, system failure is the result of two competing failure modes.

[0003] Currently, most reliability assessment models that consider the competitive failure process associated with degradation and random shocks assume a two-stage degradation process. Specifically, the degradation rate and sudden failure threshold only change when the marine engine system's performance degrades to a certain level, ignoring the impact of some shocks on system performance. In reality, each harmful shock to the competitive failure system affects the degradation rate and sudden failure threshold to some extent. These values are not fixed; rather, they are linked to the shock's amplitude and will change with the arrival of the harmful shock. Consequently, existing marine engine system reliability assessments often yield inaccurate results. Summary of the Invention

[0004] The purpose of the present invention is to address the problem of inaccurate reliability evaluation results of marine engine systems in the prior art and to propose a reliability evaluation method for marine engine systems taking external impacts into consideration.

[0005] The technical solution adopted by the present invention to solve the above technical problems is:

[0006] The reliability assessment method of a marine engine system under external impact includes the following steps:

[0007] Step 1: Set the degradation failure threshold D S , when the overall degradation of the marine engine system exceeds the degradation failure threshold D S When the marine engine system fails due to degradation, the internal continuous degradation amount X(t) of the degradation rate under the impact and the sudden increase degradation amount S(t) caused by the impact are obtained. The sum of the internal continuous degradation amount X(t) of the degradation rate under the impact and the sudden increase degradation amount S(t) caused by the impact is the overall performance degradation amount X of the marine engine system.S (t), and then the impact arrival time follows the exponential distribution, and combined with the overall performance degradation of the marine engine system X S (t) Obtaining the reliability function of the marine engine system without degradation failure under external harmful impact;

[0008] Step 2: Set the sudden failure threshold When the external impact amplitude W of the marine engine system at a certain moment j Exceeding the sudden failure threshold When the marine engine system fails suddenly, then the reliability function of the marine engine system without sudden failure under extreme impact is obtained. The sudden failure threshold D H The changing rule of Among them, D L is the critical threshold, W j >D L , w represents the shock amplitude of the marine engine system experiencing harmful shock, is the next burst failure threshold;

[0009] Step 3: Obtain the probability of the marine engine system experiencing m harmful shocks. Then, based on the probability of the marine engine system experiencing m harmful shocks and combining the reliability function of the marine engine system not experiencing degradation failure under external harmful shocks and the reliability function of the marine engine system not experiencing sudden failure under extreme shocks, obtain the total reliability function of the marine engine system not experiencing failure.

[0010] Step 4: using the Monte Carlo multiple integration calculation method to solve the total reliability function of the marine engine system without failure, and obtain the reliability curve of the marine engine system;

[0011] Step 5: Process the marine engine system to be evaluated using steps 3 and 4 to obtain a reliability curve of the marine engine system to be evaluated, and obtain a system evaluation result, i.e., the mean time between failures (MTBF) of the marine engine system, based on the reliability curve of the marine engine system to be evaluated.

[0012] Furthermore, the internal continuous degradation amount X(t) of the variable degradation rate under the impact is expressed as:

[0013]

[0014] in, is the initial degradation amount, β1 is a random variable representing the degradation rate of the first stage, β2 is a random variable representing the degradation rate of the second stage, and β m+1 is a random variable representing the degradation rate of the m+1th stage, β jis a random variable representing the degradation rate of stage j, T2-T1 is the time interval between two harmful shocks, T j -T j-1 is the time interval between two harmful shocks, and t is the time.

[0015] Furthermore, the sudden increase degradation amount S(t) caused by the impact is expressed as:

[0016]

[0017] Among them, Y j is a random variable, which represents the sudden degradation amount caused by the jth harmful impact experienced by the marine engine system during the degradation failure process.

[0018] Furthermore, the overall performance degradation of the marine engine system X S (t) is expressed as:

[0019]

[0020] Furthermore, the reliability function of the marine engine system that does not suffer degradation failure under external harmful impact is expressed as:

[0021]

[0022] Where Φ(·) is the cumulative distribution function of the standard normal distribution, N H (t) is the number of harmful shocks experienced by the marine engine system within time t, f(T1, T2,…, T m ) is the joint probability density function of the shock arrival time, T1, T2, …, T m is the arrival time of m harmful shocks, m! is T1, T2, ..., T m The number of possible sorts, are the mean and variance of the degradation rate of the marine engine system under the external harmful shock in stage j, are the mean and variance of the degradation rate of the marine engine system after it experiences the mth harmful shock from the outside, is the mean and variance of the sudden increase in degradation during the degradation process of the marine engine system under the action of external harmful shock, X S (t|T1,T2,…,T m ) is the total performance degradation of the marine engine system under the condition of m harmful shocks.

[0023] Furthermore, the specific steps of step one are:

[0024] The multi-stage variable degradation rate linear degradation process of the marine engine system is expressed as Assume that the marine engine system experiences m harmful shocks, and the arrival times of the m harmful shocks are T1, T2, …, T m Therefore, the internal degradation process of the marine engine system under extreme impact is shown in formula (1):

[0025]

[0026] in, is the initial degradation amount, β j is a random variable representing the degradation rate of stage j, T j -T j-1 is the time interval between two harmful shocks;

[0027] The linear conversion model is used to describe the variation of the degradation rate of the marine engine system under various shocks. The variation of the degradation rate is a linear function of the various shock amplitudes and is expressed as: Where j = 1, 2, ..., m, The initial degradation rate has a mean and variance of μ β and Normal distribution, A1, A2, …, A n For the impact type, Representative A i The magnitude of the impact of the species is a random variable that follows a normal distribution is a random variable with mean and variance and The normal distribution of , i = 1, 2, ..., n, where i is the type of external shock, n is the total number of external shock types, and α is the conversion coefficient between the amplitude of each shock and the change in degradation rate. Therefore, the degradation rate and degradation amount distribution at different stages are shown in formula (2):

[0028]

[0029] Define Y j is a random variable, which represents the sudden increase in degradation caused by the jth harmful shock during the degradation failure process. The linear conversion model is used to describe the sudden increase in degradation caused by various shocks. The sudden increase in degradation caused by the harmful shock can be expressed as Where y represents the random effect other than the shock, γ is the conversion coefficient between each shock amplitude and the sudden increase degradation amount, are the mean and variance of the degradation rate of the marine engine system under the external harmful shock in stage i. Therefore, the distribution of the sudden increase in degradation amount generated by the marine engine system after the jth harmful shock and the cumulative sudden increase in degradation amount calculated according to time t can be obtained as shown in formula (3):

[0030]

[0031] The total performance degradation in the degradation failure process is the sum of the internal continuous degradation and the total sudden degradation, as shown in formula (4):

[0032]

[0033] Considering that the external shock is a homogeneous Poisson distribution process with a shock arrival rate of λ, the shock arrival time obeys an exponential distribution. Combining formula (4), the reliability function of the marine engine system that does not suffer degradation failure under the action of external harmful shock is obtained as shown in formula (5):

[0034]

[0035] Furthermore, the reliability function of the sudden failure of the marine engine system under the extreme impact is expressed as:

[0036]

[0037] Where p is the conversion coefficient between each shock amplitude and the comprehensive shock amplitude of the marine engine system, N H (t) is the number of harmful shocks experienced by the marine engine system within time t, is the sudden failure threshold of the marine engine system during the first stage of shock, μ W and are the mean and variance of the external harmful shock to the marine engine system.

[0038] Furthermore, the probability of m harmful shocks occurring to the marine engine system is expressed as:

[0039]

[0040] Among them, λ H is the impact arrival rate.

[0041] Furthermore, the specific steps of step 2 are:

[0042] Define the jth impact magnitude as W j , all W j are independent and identically distributed random variables, so under the influence of various shocks Where p is the proportional coefficient, since Therefore, the distribution of external shocks is shown in formula (6):

[0043]

[0044] Assume that the initial burst failure threshold is D H, then under the condition that the failure threshold changes continuously, the probability that the marine engine system does not fail suddenly after experiencing the jth harmful impact is Where: j = 1, 2, ...; F W (·) is W j The distribution function of the sudden failure threshold is: Where W j >D L The sudden failure threshold change is described by a linear function of the difference between the impact load amplitude and the critical threshold, w is the unit change of the failure threshold, so formula (7) can be obtained:

[0045]

[0046] Therefore, the reliability function of sudden failure of marine engine system under extreme shock can be obtained as shown in formula (8):

[0047]

[0048] Furthermore, the total reliability function of the marine engine system is expressed as:

[0049]

[0050]

[0051] Among them, R s (tN H (t) = 0) is the reliability function of the marine engine system performance degradation process when there is no external harmful impact, R e (tN H (t) = 0) is the reliability function of the marine engine system without sudden failure under extreme impact when there is no external harmful impact, P(N H (t) = 0) is the probability of m harmful shocks occurring to the marine engine system when there is no external harmful shock, R s (tN H (t) = m) is the reliability function of the marine engine system without degradation failure under external harmful impact, R e (tN H (t) = m) is the reliability function of the marine engine system without sudden failure under extreme impact, P(N H (t) = m) is the probability that a harmful shock occurs m times in the marine engine system.

[0052] The beneficial effects of the present invention are:

[0053] This application divides random shocks into harmless shocks and harmful shocks. Based on the shock amplitude, the impact of harmful shocks on the degradation rate and sudden failure threshold level of the marine engine system under the extreme shock model is further considered. This is specifically reflected in three aspects: (1) The performance degradation level of the marine engine system will undergo a sudden change with the arrival of external shocks; (2) External shocks can change the degradation rate of the marine engine system. For example, due to the external shock, the working pressure or contact surface running speed of the metal contact surface increases, which increases the wear rate of the product. That is, with the external shock, the degradation rate of the marine engine system continues to change; (3) The sudden failure threshold level of the marine engine system is related to the external shock amplitude experienced. Specifically, with the external shock, the marine engine system's resistance to external shocks becomes worse, that is, the sudden failure threshold level decreases. Finally, for the marine engine system with a related competitive failure process with continuously changing degradation rate and failure threshold, a reliability model that is more in line with actual working conditions is established, thereby obtaining more accurate and reasonable reliability evaluation results.

[0054] This application fully considers the impact of external shocks on the performance degradation process of marine engine systems, finds the intrinsic connection between external shocks and the performance degradation rate and sudden failure threshold changes of marine engine systems. When evaluating the reliability of marine engine systems, the sudden changes in degradation levels caused by multiple random shocks, the increase in degradation rate, and the decrease in failure threshold in the extreme shock model should be considered simultaneously to obtain more accurate marine engine system reliability evaluation results and avoid overestimation of marine engine system reliability.

[0055] Through sensitivity analysis of the basic parameters of the model, this application can find out that different parameters have great differences in sensitivity to the reliability assessment of the marine engine system. Therefore, it can provide a reference for parameter selection when conducting reliability tests on the marine engine system. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 This is the application process diagram;

[0057] Figure 2 This is a schematic diagram of the performance degradation process of the marine engine system in this application;

[0058] Figure 3 This is a schematic diagram of the extreme impact process of the marine engine system in this application;

[0059] Figure 4 is the reliability change curve of the micro engine;

[0060] Figure 5 A comparison chart of the reliability assessment results based on the reliability curves considering the degradation rate change and the failure threshold change respectively and the model established in this application;

[0061] Figure 6 Schematic diagram of sensitivity analysis of parameters affecting degradation rate and failure threshold Figure 1 ;

[0062] Figure 7 Schematic diagram of sensitivity analysis of parameters affecting degradation rate and failure threshold Figure 2 . DETAILED DESCRIPTION

[0063] It should be noted that, unless there is any conflict, the various embodiments disclosed in this application can be combined with each other.

[0064] Specific implementation method 1: refer to Figure 1 Specifically, this embodiment provides a method for evaluating the reliability of a marine engine system under external impact. System failure is the result of competition between degradation failure and sudden failure. When the performance degradation exceeds a fixed degradation failure threshold D S When the external impact amplitude exceeds the sudden failure threshold D H At (t), the marine engine system fails suddenly.

[0065] Step 1: Analyze the actual working conditions and operating status of the marine engine system, design a reasonable mathematical model to describe the performance degradation process and sudden failure process of the marine engine system, and analyze the mutual influencing factors of the two competitive failure processes of the marine engine system. The performance degradation process of the marine engine system at different stages is proposed to be represented by a general degradation path model; the correlation between external shocks and internal degradation is as follows: Figure 2 and Figure 3 As shown in Figure 2, the performance degradation process of a marine engine system includes continuous degradation with a variable degradation rate and sudden degradation caused by external shocks. m (m=1,2,…) is the time when the mth harmful impact occurs, Y m (m=1, 2, ...) represents the sudden degradation amount caused by the mth harmful impact experienced by the marine engine system. Figure 3 In the extreme shock process, the shock amplitude is in [0,D L ) is harmless shock, and the shock amplitude is [D L ,+∞) interval is a harmful shock, where D L is the critical threshold and its amplitude is higher than D L The impact of W will affect the degradation failure process and sudden failure threshold of the marine engine system. m (m = 1, 2, ...) represents the impact amplitude of the mth harmful impact experienced by the marine engine system. Under the influence of external harmful impact, the degradation rate and sudden failure threshold of the marine engine system at different stages change.

[0066] Step 2: Consider the degradation failure process analysis of the marine engine system under the influence of external impact, such as Figure 2 As shown in the figure, when the overall degradation of the marine engine system exceeds the degradation failure threshold D S When the marine engine system fails, the degradation of the overall performance of the marine engine system will occur. S (t) is the sum of the internal continuous degradation rate X(t) and the sudden degradation rate S(t) caused by the impact. The number of harmful impacts experienced by the marine engine system within time t is defined as N. H (t).

[0067] The general degradation path model of the marine engine system is expressed as Where: represents the initial degradation amount; β is a random variable representing the initial degradation rate; degradation rate The reliability function of the performance degradation process of the marine engine system without external harmful impact is shown in formula (1):

[0068]

[0069] When the degradation process is under the influence of harmful shocks, the degradation rate of the marine engine system will continue to change and increase suddenly. Under the influence of various external shocks, the degradation rate of the marine engine system increases in different degradation stages. j is a random variable representing the degradation rate of the jth stage. A linear conversion model is proposed to describe the variation of the degradation rate of the marine engine system under various shocks. The variation of the degradation rate is a linear function of the various shock amplitudes and can be expressed as: Where j = 1, 2, ..., m; A1,A2,…,A n is the impact type; Representative A i The magnitude of the impact of the species is a random variable that follows a normal distribution α is the conversion coefficient between the amplitude of each impact and the change in degradation rate, and its value is estimated based on degradation data, life testing, engineering evaluation, etc. Therefore, the degradation rate distribution at different stages can be obtained as shown in formula (2):

[0070]

[0071] The multi-stage linear degradation process of the marine engine system with variable degradation rate can be expressed as Assume that the marine engine system experiences m harmful shocks, and the arrival times of the m harmful shocks are T1, T2, …, T m Therefore, the continuous degradation process of the marine engine system under extreme impact is shown in formula (3):

[0072]

[0073] Where, T j -T j-1 is the time interval between two harmful shocks. Therefore, the distribution of internal continuous degradation under external shocks is shown in formula (4):

[0074]

[0075] Define Y j is a random variable, which represents the sudden increase in degradation caused by the jth harmful shock during the degradation failure process. The linear conversion model is used to describe the sudden increase in degradation caused by various shocks. The sudden increase in degradation caused by the harmful shock can be expressed as Where y represents the random effect other than the shock, γ is the conversion coefficient between each impact amplitude and the sudden increase degradation amount. Therefore, the distribution of the sudden increase degradation amount generated by the marine engine system after the jth harmful impact and the cumulative sudden increase degradation amount calculated according to time t can be obtained as shown in formula (5):

[0076]

[0077] The total performance degradation of the degradation failure process is shown in formula (6):

[0078]

[0079] You can get X S The distribution of (t) is obtained, and the reliability function of the marine engine system without degradation failure under external harmful impact is shown in formula (7):

[0080]

[0081] Since the external shock is a homogeneous Poisson distribution process with a shock arrival rate of λ, the shock arrival time follows an exponential distribution, and the joint probability density function of the shock arrival time is shown in formula (8):

[0082]

[0083] Therefore, the degradation failure reliability function of the marine engine system is shown in formula (9):

[0084]

[0085] Here, d represents the integral.

[0086] Step 3: Consider the sudden failure process analysis of the marine engine system under the influence of external shock. When the external shock amplitude of the marine engine system at a certain moment exceeds the failure threshold, the marine engine system will fail suddenly. Define the magnitude of the j-th shock as W j , all W j are independent and identically distributed random variables, so under various shocks W j It can be expressed as Where p is the conversion coefficient between each shock amplitude and the comprehensive shock amplitude of the marine engine system. Therefore, the distribution of the shock can be obtained as shown in formula (10):

[0087]

[0088] Assume that the initial burst failure threshold is D H , then under the condition that the failure threshold changes continuously, the probability that the marine engine system does not fail suddenly after experiencing the jth harmful impact is Where j = 1, 2, ...; F W (·) is W j The distribution function of . In time t, when there is no harmful impact, the reliability of sudden failure of the marine engine system is R e (t|N H (t)=0)=1; when there is a harmful shock, it is assumed that the failure threshold changes as follows: Where W j >D L The sudden failure threshold change is described by a linear function of the difference between the impact load amplitude and the critical threshold, w is the unit change of the failure threshold, and formula (11) can be obtained:

[0089]

[0090] Therefore, the reliability function of the marine engine system without sudden failure under extreme impact is shown in formula (12):

[0091]

[0092] Step 4: Consider the reliability modeling of the competitive failure process with variable degradation rate and failure threshold. Since the impact process is a homogeneous Poisson process with an arrival rate of λ, the number of harmful impacts N within time t is defined as H (t) = m, so we can know N H (t) is subject to λ H =λ(1-F W (D L )) is a homogeneous Poisson process, then the probability of m harmful shocks occurring in the marine engine system is as shown in formula (13):

[0093]

[0094] Since the degradation increment of the marine engine system itself and the sudden degradation increment caused by external shocks are independent of each other, and the failure of the marine engine system is the result of the competition between degradation failure and sudden failure, the reliability function of the marine engine system is shown in Equation (14) by combining the analysis of the conditional reliability functions of all degradation failure processes and sudden failure processes:

[0095]

[0096] In summary, the overall reliability evaluation model of the marine engine system can be obtained as shown in formula (15):

[0097]

[0098] Step 5: Use the Monte Carlo multiple integral calculation method to solve the multiple integrals. The specific operation method is as follows.

[0099] a) Assign specific values to the operating time t of the marine engine system and the number of harmful shocks m experienced by the marine engine system, and then define i=1:N, run Monte Carlo simulation steps b)-d);

[0100] b) Generate N groups of m uniformly distributed random numbers at (0, t) and define the impact arrival times T1, T2, ..., T m is the order statistic of m independent random variables;

[0101] c) Using the generated T1, T2, ..., T m The value of G i (t,m) is the value of the integrand, and the volume of the entire integration domain is V S =t m ;

[0102] d) Stop the simulation until i=N, and the approximate value of the multiple integral can be obtained as follows: Where m! represents T1, T2, ..., T m Possible sorting number. Obtain the reliability curve of the marine engine system

[0103] Step 6: Substitute the parameter values of the marine engine system into the marine engine system reliability function formula (15) obtained in step 4, realize the reliability evaluation of the marine engine system with competitive failure under various external shocks considering the variable degradation rate and failure threshold, and complete the sensitivity analysis of the influence of each model parameter on the reliability of the marine engine system.

[0104] The parameters to be measured are input into step 4, and step 5 is used to generate the marine engine system reliability curve. The evaluation result (marine engine system failure-free time) is then obtained based on the marine engine system reliability curve. Reliability: The probability that a component will operate without failure within its specified lifespan and under specified operating conditions. Reliability is a function of time.

[0105] Mean time between failures

[0106] The following is an experimental verification of this application using a certain model of engine as the object:

[0107] Analysis of the failure mechanism of a certain engine model revealed that surface wear between gears and pin joints was the primary cause of engine degradation and failure. Wear at these locations, in particular, can easily lead to pin joint fracture, resulting in loss of engine operation and sudden failure. Furthermore, external impacts can cause wear debris to form between gears and pin joints, accelerating the wear rate. Table 1 lists the relevant performance parameters of this micro-engine.

[0108] Table 1 Engine system reliability analysis parameter values

[0109]

[0110] Substitute the above parameters into formula (15), that is, the competitive failure system reliability assessment model considering the variable degradation rate and failure threshold of various external shocks obtained in step 4. Use the Monte Carlo simulation method with multiple integrals in step 5 to obtain the product reliability function R(t), thus completing the competitive failure system reliability assessment.

[0111] Under the condition of extreme shock, when the system is calculated by formula (15), the number of external harmful shocks m is defined as 50, the number of samples N is 10000, and the system reliability is calculated by combining the data in Table 1 with the Monte Carlo simulation algorithm, and the result is: Figure 4 The reliability curve of the micro-engine system life is shown. Engineering operators can use the reliability curve to judge system performance. When the system reliability falls below the recognized safety range, necessary reliability maintenance is required.

[0112] The reliability model established in this application, which has a dual impact of random shock on system degradation failure and sudden failure, is denoted as M1; the reliability model that only considers the impact of random shock on the system degradation failure process, that is, the situation where a sudden degradation increment and a sudden increase in the system degradation rate are generated, is denoted as M2; the reliability model that only considers the impact of random shock on the system sudden failure process, that is, the system sudden failure threshold changes continuously with the arrival of shock, is denoted as M3. Figure 5The model proposed in this chapter comprehensively considers the simultaneous changes in the performance degradation level, degradation rate, and sudden failure threshold under the influence of various random shocks. It can be seen that if the multiple impacts of shocks on the system are not fully considered, the system reliability will be overestimated. Therefore, the reliability model established in this application can improve the accuracy of system reliability assessment to a certain extent.

[0113] The parameter sensitivity analysis of the established reliability assessment model is carried out, and the results are as follows: Figure 6 and Figure 7 As shown. The degradation rate change law model established in this application shows that the change in degradation rate has a relatively small impact on the system in the early stage of system operation, and then gradually increases, especially in the later stage of system operation, where it has a significant impact on reliability assessment. The failure threshold change law model established in this application shows that the change in sudden failure threshold has a significant impact on reliability assessment in the early stage of system operation, and then the impact gradually decreases and can be ignored in the late stage of system operation.

[0114] Compared with the prior art, the present application only considers the performance degradation process of the system, analyzes the performance degradation process, and thus evaluates the reliability of the system, ignoring that the system may be subjected to external shocks during normal operation and may experience sudden failures under the action of external shocks. The present application considers the reliability evaluation of a competitive failure system in which degradation failures and sudden failures coexist under the action of multiple external shocks. External shocks not only affect the performance degradation process of the system, causing changes in the system degradation rate and a sudden increase in the amount of performance degradation, but also reduce the sudden failure threshold, that is, after experiencing a harmful shock, the system's ability to resist external shocks will be weakened.

[0115] It should be noted that the specific embodiments are merely explanations and illustrations of the technical solutions of the present invention and cannot be used to limit the scope of protection. Any minor changes made based on the claims and description of the present invention shall still fall within the scope of protection of the present invention.

Claims

1. A method for evaluating the reliability of a marine engine system under external impact, characterized by The following steps are involved: Step 1: Set the degradation failure threshold D S , when the overall degradation of the marine engine system exceeds the degradation failure threshold D S When the marine engine system fails due to degradation, the internal continuous degradation amount X(t) of the degradation rate under the impact and the sudden increase degradation amount S(t) caused by the impact are obtained. The sum of the internal continuous degradation amount X(t) of the degradation rate under the impact and the sudden increase degradation amount S(t) caused by the impact is the overall performance degradation amount X of the marine engine system. S (t), and then the impact arrival time follows the exponential distribution, and combined with the overall performance degradation of the marine engine system X S (t) Obtaining the reliability function of the marine engine system without degradation failure under external harmful impact; Step 2: Set the sudden failure threshold When the external impact amplitude W of the marine engine system at a certain moment j Exceeding the sudden failure threshold When the marine engine system fails suddenly, then the reliability function of the marine engine system without sudden failure under extreme impact is obtained. The sudden failure threshold D H The changing rule of Among them, D L is the critical threshold, W j >D L , w represents the shock amplitude of the marine engine system experiencing harmful shock, is the next burst failure threshold; Step 3: Obtain the probability of the marine engine system experiencing m harmful shocks. Then, based on the probability of the marine engine system experiencing m harmful shocks and combining the reliability function of the marine engine system not experiencing degradation failure under external harmful shocks and the reliability function of the marine engine system not experiencing sudden failure under extreme shocks, obtain the total reliability function of the marine engine system not experiencing failure. Step 4: using the Monte Carlo multiple integration calculation method to solve the total reliability function of the marine engine system without failure, and obtain the reliability curve of the marine engine system; Step 5: Process the marine engine system to be evaluated using steps 3 and 4 to obtain a reliability curve of the marine engine system to be evaluated, and obtain a system evaluation result, i.e., the mean time between failures (MTBF) of the marine engine system, based on the reliability curve of the marine engine system to be evaluated.

2. The method for evaluating the reliability of a marine engine system under external impact according to claim 1, characterized in that The internal continuous degradation amount X(t) of the variable degradation rate under the impact is expressed as: in, is the initial degradation amount, β1 is a random variable representing the degradation rate of the first stage, β2 is a random variable representing the degradation rate of the second stage, and β m+1 is a random variable representing the degradation rate of the m+1th stage, β j is a random variable representing the degradation rate of stage j, T2-T1 is the time interval between two harmful shocks, T j -T j-1 is the time interval between two harmful shocks, and t is the time.

3. The method for evaluating the reliability of a marine engine system under external impact according to claim 2 is characterized in that The sudden increase in degradation S(t) caused by the impact is expressed as: Among them, Y j is a random variable, which represents the sudden degradation amount caused by the jth harmful impact experienced by the marine engine system during the degradation failure process.

4. The method for evaluating the reliability of a marine engine system under external impact according to claim 3 is characterized in that The overall performance degradation of the marine engine system X S (t) is expressed as:

5. The method for evaluating the reliability of a marine engine system under external impact according to claim 4 is characterized in that The reliability function of the marine engine system that does not fail under external harmful impact is expressed as: Where Φ(·) is the cumulative distribution function of the standard normal distribution, N H (t) is the number of harmful shocks experienced by the marine engine system within time t, f(T1, T2,…, T m ) is the joint probability density function of the shock arrival time, T1, T2, …, T m is the arrival time of m harmful shocks, m! is T1, T2, ..., T m The number of possible sorts, are the mean and variance of the degradation rate of the marine engine system under the external harmful shock in stage j, is the mean and variance of the degradation rate of the marine engine system after it experiences the mth harmful shock from the outside, μ Y 、 is the mean and variance of the sudden increase in degradation during the degradation process of the marine engine system under the action of external harmful shock, X S (t|T1,T2,…,T m ) is the total performance degradation of the marine engine system under the condition of m harmful shocks.

6. The method for evaluating the reliability of a marine engine system under external impact according to claim 5 is characterized in that The specific steps of step one are: The multi-stage variable degradation rate linear degradation process of the marine engine system is expressed as Assume that the marine engine system experiences m harmful shocks, and the arrival times of the m harmful shocks are T1, T2, …, T m Therefore, the internal degradation process of the marine engine system under extreme impact is shown in formula (1): in, is the initial degradation amount, β j is a random variable representing the degradation rate of stage j, T j -T j-1 is the time interval between two harmful shocks; The linear conversion model is used to describe the variation of the degradation rate of the marine engine system under various shocks. The variation of the degradation rate is a linear function of the various shock amplitudes and is expressed as: Where j = 1, 2, ..., m, The initial degradation rate has a mean and variance of μ β and Normal distribution, A1, A2, …, A n For the impact type, Representative A i The magnitude of the impact of the species is a random variable that follows a normal distribution is a random variable with mean and variance and The normal distribution of , i = 1, 2, ..., n, where i is the type of external shock, n is the total number of external shock types, and α is the conversion coefficient between the amplitude of each shock and the change in degradation rate. Therefore, the degradation rate and degradation amount distribution at different stages are shown in formula (2): Define Y j is a random variable, which represents the sudden increase in degradation caused by the jth harmful shock during the degradation failure process. The linear conversion model is used to describe the sudden increase in degradation caused by various shocks. The sudden increase in degradation caused by the harmful shock can be expressed as Where y represents the random effect other than the shock, γ is the conversion coefficient between each shock amplitude and the sudden increase degradation amount, are the mean and variance of the degradation rate of the marine engine system under the external harmful shock in stage i. Therefore, the distribution of the sudden increase in degradation amount generated by the marine engine system after the jth harmful shock and the cumulative sudden increase in degradation amount calculated according to time t can be obtained as shown in formula (3): The total performance degradation in the degradation failure process is the sum of the internal continuous degradation and the total sudden degradation, as shown in formula (4): Considering that the external shock is a homogeneous Poisson distribution process with a shock arrival rate of λ, the shock arrival time obeys an exponential distribution. Combining formula (4), the reliability function of the marine engine system that does not suffer degradation failure under the action of external harmful shock is obtained as shown in formula (5):

7. The method for evaluating the reliability of a marine engine system under external impact according to claim 6, characterized in that The reliability function of sudden failure of the marine engine system under the extreme impact is expressed as: Where p is the conversion coefficient between each shock amplitude and the comprehensive shock amplitude of the marine engine system, N H (t) is the number of harmful shocks experienced by the marine engine system within time t, D H1 is the sudden failure threshold of the marine engine system during the first stage of shock, μ W and are the mean and variance of the external harmful shock to the marine engine system.

8. The method for evaluating the reliability of a marine engine system under external impact according to claim 7 is characterized in that The probability of m harmful shocks occurring to the marine engine system is expressed as: Among them, λ H is the impact arrival rate.

9. The method for evaluating the reliability of a marine engine system under external impact according to claim 8, characterized in that The specific steps of step 2 are: Define the jth impact magnitude as W j , all W j are independent and identically distributed random variables, so under the influence of various shocks Where p is the proportional coefficient, since Therefore, the distribution of external shocks is shown in formula (6): Assume that the initial burst failure threshold is D H , then under the condition that the failure threshold changes continuously, the probability that the marine engine system does not fail suddenly after experiencing the jth harmful impact is Where: j = 1, 2, ...; F W (·) is W j The distribution function of the sudden failure threshold is: Where W j >D L The sudden failure threshold change is described by a linear function of the difference between the impact load amplitude and the critical threshold, w is the unit change of the failure threshold, so formula (7) can be obtained: Therefore, the reliability function of sudden failure of marine engine system under extreme shock can be obtained as shown in formula (8):

10. The method for evaluating the reliability of a marine engine system under external impact according to claim 9, characterized in that The total reliability function of the marine engine system is expressed as: Among them, R s (tN H (t) = 0) is the reliability function of the marine engine system performance degradation process when there is no external harmful impact, R e (tN H (t) = 0) is the reliability function of the marine engine system without sudden failure under extreme impact when there is no external harmful impact, P(N H (t) = 0) is the probability of m harmful shocks occurring to the marine engine system when there is no external harmful shock, R s (tN H (t) = m) is the reliability function of the marine engine system without degradation failure under external harmful impact, R e (tN H (t) = m) is the reliability function of the marine engine system without sudden failure under extreme impact, P(N H (t) = m) is the probability that a harmful shock occurs m times in the marine engine system.

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