Ellipsoid model-based reliability analysis method for magnetorheological fluid brake
By introducing an ellipsoidal model and Markov chain into fault tree analysis, the problem of inaccurate fault probability estimation caused by insufficient sample data is solved, and high-precision fault rate estimation is achieved in the absence of data.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- TAIYUAN UNIVERSITY OF SCIENCE AND TECHNOLOGY
- Filing Date
- 2022-11-02
- Publication Date
- 2026-07-24
AI Technical Summary
Existing techniques in fault tree analysis lack sufficient statistical data, making it difficult to accurately estimate the failure probability of bottom events, resulting in overly conservative or inaccurate results, especially when sample data is insufficient.
By introducing the ellipsoidal model into dynamic fault tree analysis, qualitative and quantitative analysis is performed by constructing a high-dimensional ellipsoidal model and Markov chains. A small amount of sample data is used to describe the uncertainty and correlation of bottom events, thereby accurately estimating the failure probability of top events.
It can scientifically describe the failure probability of bottom events when sample data is insufficient, improve the accuracy and precision of fault tree analysis, and more accurately obtain the failure rate of top events when data is lacking in large equipment.
Smart Images
Figure CN115688580B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of mechanical component reliability analysis technology, specifically relating to a reliability analysis method for magnetorheological fluid brakes based on an ellipsoidal model. Background Technology
[0002] A fault tree is a special type of inverted tree-like logical causal logic diagram, composed of various event symbols and logic gates describing the causal relationships between events. Fault tree analysis uses the fault tree as a root tool to perform qualitative and quantitative analysis of the system, obtaining reliability data such as failure rates. Since its introduction in the last century, the fault tree method has been rapidly adopted in the field of reliability and is widely recognized as a simple and effective reliability analysis method. A dynamic fault tree refers to a fault tree containing dynamic fault gates. Dynamic fault gates can more accurately describe the sequential correlation, repairability, and hot / cold spare parts characteristics between events. Both traditional and dynamic fault trees require precise values of the probability of occurrence of underlying events. However, in practical engineering applications, sufficient statistical data is often lacking, making it impossible to provide accurate probability estimates of underlying events. Some scholars have proposed using fuzzy mathematics to study reliability data, proposing methods using fuzzy numbers to describe failure rates. However, both probabilistic reliability and fuzzy reliability are based on probability theory and require a large amount of data. Therefore, some scholars have proposed using convex set models to describe the uncertainty of data and using interval models for reliability analysis of fault trees. This method has lower data requirements and is suitable for small sample situations. The extreme values of interval probabilities obtained by the interval model require all the base events to be taken at the interval boundaries, which is rare in practice. Therefore, the results obtained are too conservative. Summary of the Invention
[0003] The purpose of this invention is to solve the aforementioned technical problems and provide a reliability analysis method for magnetorheological fluid brakes based on an ellipsoidal model. This method introduces an ellipsoidal model into the dynamic fault tree analysis process. Addressing the issue of insufficient sample data, the ellipsoidal model requires only a small amount of sample data to obtain the uncertain parameter boundaries of the data, thus better describing the probability of bottom events and improving the solution for the failure probability of top events.
[0004] To achieve the above objectives, the technical solution adopted by the present invention is as follows:
[0005] A reliability analysis method for a magnetorheological fluid brake based on an ellipsoidal model is provided. The magnetorheological fluid brake comprises a drive shaft, bearings, end caps, a brake housing, an excitation coil, magnetorheological fluid, a brake disc, a sealing ring, and a key. The steps of the reliability analysis method are as follows:
[0006] Step 1: Use fault mode diagnosis to classify the faults in the magnetorheological fluid brake and determine the fault severity level;
[0007] 1.1: Based on the working mode and characteristics of the magnetorheological fluid brake, determine the typical failure modes of the magnetorheological fluid brake and the failures of each component;
[0008] 1.2: Based on the fault types of each component of the magnetorheological fluid brake, determine the cause, severity level, and repair method of each component fault of the magnetorheological fluid brake;
[0009] Step 2: Based on the analysis results of the failure modes and hazards of the magnetorheological fluid brake, a dynamic fault tree is established, and the dynamic fault tree is modularly decomposed into a dynamic fault subtree module and a static fault subtree module.
[0010] 2.1: Based on the analysis results of the impact and hazard of the failure modes of magnetorheological fluid brakes, a dynamic fault tree for magnetorheological fluid brakes is constructed with the failure of the magnetorheological fluid brake as the top event, the failure modes of the three brakes and the failures of the nine subsystems as intermediate events, and the failures of each component as the bottom event.
[0011] 2.2: The dynamic fault tree is modularized using a linear search algorithm, decomposing it into independent dynamic fault subtree modules and static fault subtree modules;
[0012] Step 3: Based on small sample data, obtain the upper and lower extreme values of the failure rates of each component of the magnetorheological fluid brake, construct interval models of the failure rates of each bottom event, and convert the interval models into high-dimensional ellipsoidal models using the minimum volume enclosing ellipsoid modeling method, thereby constructing ellipsoidal models of the top events of each failure subtree:
[0013]
[0014] in: Let X be an n-dimensional ellipsoidal model, where X is an ellipsoidal variable. 0 Let R be the center of the ellipsoid, Ω be the characteristic matrix, and R be the eigenvalue. n It is the set of n-dimensional real numbers;
[0015] Step 4: Use the BDD (Binary Decision Diagram) method and Markov chains to perform qualitative and quantitative analysis and solve the dynamic fault tree;
[0016] 4.1: Convert the dynamic fault subtree module into a Markov chain, and substitute the ellipsoid model constructed in step 3 into the solution formula of the Markov chain to obtain the failure rate of the top event of the dynamic fault subtree.
[0017]
[0018] In the formula: λ 0,1 λ is the transition rate from the normal state "0" to the failure state "Fa". 0,1 >0, λ 0,NFλ is the transition rate from the normal state "0" to the non-failure state "NF". 0,NF >0, This represents the failure rate of the top event T of a chain of length n after a working time t.
[0019] 4.2: Solving for the remaining static fault subtree using BDD;
[0020] 4.3: The solution results of each dynamic fault subtree and static fault subtree are used as the base events of the new fault tree. The new fault tree is solved, and finally the failure probability of the top event is obtained.
[0021] Furthermore, the three brake failure modes in step 2.1 are brake failure, brake release failure, and brake performance degradation.
[0022] Furthermore, the top event is brake failure; the intermediate events are brake failure, brake release failure, decreased braking performance, brake disc failure, magnetic circuit failure, magnetorheological fluid degradation, magnetorheological fluid leakage, decreased magnetic induction intensity, brake disc failure, excitation coil failure, sealing ring failure, and excitation coil failure; the bottom event is drive shaft breakage, bracket damage, bearing jamming, uninterrupted power supply to the excitation coil, brake disc jamming, decreased brake disc friction, magnetorheological fluid loss, key damage, magnetic circuit control failure, magnetorheological fluid aging, excessively high braking temperature, excessively large magnetorheological fluid gap, contaminated magnetorheological fluid, end cap damage, bolt damage, demagnetization of the brake disc drive shaft, brake disc I failure, brake disc II failure, coil I failure, coil II failure, coil III failure, excessive load, normal aging, coil I failure, coil II failure, and coil III failure.
[0023] Furthermore, for large equipment lacking data, with unclear fault data, or where reliability testing is impossible, the fault data of its components and systems can be obtained by taking the maximum and minimum values of the distribution range of the bottom events through a small number of tests or component tests. This yields the interval model of the occurrence of the bottom events, and through the failure logic relationship between different bottom events, the ellipsoidal model of the top events can be obtained.
[0024] The beneficial effects of this invention are:
[0025] This invention introduces an ellipsoidal model to describe the uncertainty of the bottom events in a dynamic fault tree. This model can more scientifically describe the failure probability of bottom events when sample data is insufficient or unavailable. The ellipsoidal model can also represent the correlation between bottom events, which can more accurately describe the common cause failures among bottom events, and thus more accurately obtain the failure rate of the analysis model. Attached Figure Description
[0026] Figure 1 This is a flowchart of the present invention;
[0027] Figure 2This is a schematic diagram of the magnetorheological fluid brake of the present invention;
[0028] Figure 3 This invention provides a dynamic fault tree model for the braking failure of the magnetorheological fluid brake.
[0029] Figure 4 This is a dynamic fault tree model for the release failure of the magnetorheological fluid brake in this invention;
[0030] Figure 5 This is a dynamic fault tree model for the deterioration of braking performance of the magnetorheological fluid brake of the present invention;
[0031] Figure 6 This invention prioritizes the conversion of PAND gates into Markov chains.
[0032] Figure 7 This invention provides a process for converting a Sequential Related Gate (SEQ) into a Markov Chain.
[0033] Figure 8 This invention relates to the process of converting functionally dependent gates (FDEPs) into Markov chains.
[0034] Figure 9 This invention relates to the process of converting a cold standby door (CSP) into a Markov chain.
[0035] Figure 10 This invention relates to the process of converting a Warm Spare Gate (WSP) into a Markov chain.
[0036] Figure 11 This invention relates to the process of converting a hot standby gate (HSP) into a Markov chain.
[0037] In the diagram: A, B, and C represent bottom events; S represents a backup component in the backup door; T represents a top event; 1 indicates a fault; 0 indicates normal; Fa indicates that the top event has occurred; Op indicates that the top event has not occurred; and the symbols on the transfer path indicate that the corresponding event has failed. Detailed Implementation
[0038] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.
[0039] like Figure 1 and Figure 2 As shown in this embodiment, a reliability analysis method for a magnetorheological fluid brake based on an ellipsoidal model is described. The magnetorheological fluid brake comprises a drive shaft 1, a bearing 2, an end cap 3, a brake housing 4, an excitation coil 5, a magnetorheological fluid 6, a brake disc 7, a sealing ring 8, and a key 9. The steps of the reliability analysis method are as follows:
[0040] Step 1: Use fault mode diagnosis to classify the faults in the magnetorheological fluid brake and determine the fault severity level;
[0041] 1.1: Based on the working mode and characteristics of the magnetorheological fluid brake, determine the typical failure modes of the magnetorheological fluid brake and the failures of each component; Table 1 shows the severity level of the failure modes.
[0042] Table 1 Failure Mode Severity Levels
[0043] I Disaster Brake damaged and lost function Ⅱ Deadly The brake was severely damaged. III moderate Brake performance deterioration IV mild It will not lead to the above three categories, but it will lead to unplanned maintenance.
[0044] 1.2: Based on the fault types of each component of the magnetorheological fluid brake, determine the fault causes, hazard levels, and repair methods of each component of the magnetorheological fluid brake, as shown in Table 2;
[0045] Table 2. FMECA Results for Magnetorheological Fluid Brakes
[0046]
[0047] Step 2: Based on the Fault Mode Effects and Criticality Analysis (FMECA) results of the magnetorheological fluid brake, a dynamic fault tree is established, and the dynamic fault tree is modularly decomposed into a dynamic fault subtree module and a static fault subtree module.
[0048] 2.1: Based on the FMECA results of the magnetorheological fluid brake, the event is numbered with the brake failure as the top event, the three brake failure modes (brake failure, brake release failure, and brake performance degradation) and nine subsystem failures as intermediate events, and the failures of individual components as bottom events. The specific event numbers are shown in Table 3. A dynamic fault tree for the magnetorheological fluid brake is constructed, as follows: Figure 3 , 4 As shown in Figure 5, Figure 3 , 4 The event codes in 5 are the same as those in Table 3;
[0049] Table 3. Correspondence between event codes and events
[0050] T Brake failure X1 Drive shaft broken X14 End cap damage M1 Brake failure X2 Bracket Damage X15 Bolt damage M2 Brake release failure X3 Bearing stuck X16 Brake disc drive shaft demagnetization M3 Decreased braking performance X4 The excitation coil is not energized X17 Brake disc I failure M4 Brake disc failure X5 Brake disc stuck X18 Brake disc II failure M5 Magnetic circuit fault X6 brake disc friction decreases X19 Coil I failure M6 magnetorheological fluid degradation X7 Magnetorheological fluid loss X20 Coil II failure M7 magnetorheological fluid leakage X8 Key destruction X21 Coil III failure M8 Decrease in magnetic induction intensity X9 Magnetic circuit control failure X22 Excessive load M9 Brake disc failure X10 Magnetorheological fluid aging X23 Normal aging M10 Excitation coil failure X11 Brake temperature too high X24 Coil I fault M11 Sealing ring failure X12 Excessive gap in magnetorheological fluid X25 Coil II fault M12 Excitation coil fault X13 Magnetorheological fluid contaminated X26 Coil III fault
[0051] In the table, T is the top event, M1…M12 are intermediate events, and X1-X26 are bottom events.
[0052] Figure 3The connection relationships of the dynamic fault tree model of the magnetorheological fluid brake failure shown are as follows: brake disc I failure and brake disc II failure are connected to brake disc failure through a hot standby gate; brake disc failure and key damage are connected to brake disc failure through an OR gate; coil I, coil II and coil III failures are connected to excitation coil failure through a hot standby gate; magnetic circuit control failure and excitation coil failure are connected to magnetic circuit failure through an OR gate; brake disc failure, magnetic circuit failure, drive shaft breakage and bracket damage are connected to brake failure through an OR gate.
[0053] Figure 4 The connection relationships in the dynamic fault tree model of the magnetorheological fluid brake release failure shown are as follows: bearing jamming, uninterrupted excitation coil and brake disc jamming are connected through an OR gate to the release failure.
[0054] Figure 5 The connection relationships in the dynamic fault tree model of the deterioration of the braking performance of the magnetorheological fluid brake shown are as follows: magnetorheological fluid aging, excessive braking temperature, excessive magnetorheological fluid gap, and magnetorheological fluid contamination are connected to magnetorheological fluid degradation through an OR gate; excessive brake load and normal aging of the sealing ring are connected to sealing ring failure through an OR gate; sealing ring failure, end cap damage, and bolt damage are connected to magnetorheological fluid leakage through an OR gate; failures of coil I, coil II, and coil III are connected to excitation coil failure through an OR gate; excitation coil failure and demagnetization of the brake disc drive shaft are connected to decreased magnetic induction intensity through an OR gate; magnetorheological fluid degradation, magnetorheological fluid leakage, decreased magnetic induction intensity, decreased brake disc friction, and magnetorheological fluid loss are connected to deterioration of braking performance through an AND gate.
[0055] 2.2: Using a linear search algorithm, the dynamic fault tree is modularized, decomposing it into independent dynamic fault subtree modules and static fault subtree modules. The dynamic fault subtree is as follows: Figure 3 As shown in Figures 4 and 5;
[0056] Step 3: Based on the existing small sample data, obtain the upper and lower extreme values of the failure rate of each component of the magnetorheological fluid brake, construct the interval model of each bottom event failure rate, and convert the interval model into a high-dimensional ellipsoid model by the minimum volume enclosing ellipsoid modeling method, and then construct the ellipsoid model of the top event of each fault subtree.
[0057] Assume the uncertain parameter X is determined from the sample data. i The number of intervals (i = 1, 2, ..., n) is
[0058]
[0059] In the formula, The lower bound of the interval, This is the upper bound of the interval;
[0060] Interval number X i midpoint radius They are respectively
[0061]
[0062]
[0063] The covariance matrix of the interval numbers is expressed as:
[0064]
[0065] Both the interval model and the ellipsoidal model are symmetric, and the center of the interval number is the center of the ellipsoid.
[0066]
[0067] The covariance matrix of the circumscribing ellipsoid is
[0068]
[0069] The inverse of the covariance matrix can be written as r, the length of the semi-axis. i expression
[0070]
[0071] The circumscribed ellipsoid is expressed as
[0072]
[0073] The obtained ellipsoid model is:
[0074]
[0075] in: Let X be an n-dimensional ellipsoidal model, where X is an ellipsoidal variable. 0 Let R be the center of the ellipsoid, Ω be the characteristic matrix, and R be the eigenvalue. n It is the set of n-dimensional real numbers;
[0076] Step 4: Use the BDD (Binary Decision Diagram) method and Markov chains to perform qualitative and quantitative analysis and solve the dynamic fault tree;
[0077] 4.1: The dynamic fault subtree module is transformed into a Markov chain, that is, using... Figures 6 to 11 Each dynamic fault gate shown is converted into a Markov chain method. The ellipsoidal model constructed in step 3 is substituted into the solution formula of the Markov chain to obtain the failure rate of the top event of the dynamic fault subtree.
[0078]
[0079] In the formula: λ 0,1λ is the transition rate from the normal state "0" to the failure state "Fa". 0,1 >0, λ 0,NF λ is the transition rate from the normal state "0" to the non-failure state "NF". 0,NF >0, This represents the failure rate of the top event T of a chain of length n after a working time t.
[0080] 4.2: Solving for the remaining static fault subtree using BDD;
[0081] 4.3: The solution results of each dynamic fault subtree and static fault subtree are used as the base events of the new fault tree. The new fault tree is solved, and finally the failure probability of the top event is obtained.
[0082] The top event is brake failure; the intermediate events are brake failure, brake release failure, decreased braking performance, brake disc failure, magnetic circuit failure, magnetorheological fluid degradation, magnetorheological fluid leakage, decreased magnetic induction intensity, brake disc failure, excitation coil failure, sealing ring failure, and excitation coil failure; the bottom event is drive shaft breakage, bracket damage, bearing jamming, uninterrupted power supply to the excitation coil, brake disc jamming, decreased brake disc friction, magnetorheological fluid loss, key damage, magnetic circuit control failure, magnetorheological fluid aging, excessively high braking temperature, excessively large magnetorheological fluid gap, contaminated magnetorheological fluid, end cap damage, bolt damage, demagnetization of the brake disc drive shaft, brake disc I failure, brake disc II failure, coil I failure, coil II failure, coil III failure, excessive load, normal aging, coil I failure, coil II failure, and coil III failure.
[0083] For large equipment lacking data, with unclear fault data, or where reliability testing is impossible, this invention obtains the interval model of the occurrence of bottom events by taking the maximum and minimum values of the distribution interval of bottom events from a small number of tests or component tests. Then, through the failure logic relationship between different bottom events, an ellipsoidal model of the top event is obtained.
Claims
1. A reliability analysis method for a magnetorheological fluid brake based on an ellipsoidal model, characterized in that the magnetorheological fluid brake comprises a drive shaft, bearings, end caps, a brake housing, an excitation coil, magnetorheological fluid, a brake disc, a sealing ring, and a key, and the reliability analysis method comprises the following steps: Step 1: Use fault mode diagnosis to perform fault stratification on the magnetorheological fluid brake and determine the fault hazard level; 1.1: Based on the working mode and characteristics of the magnetorheological fluid brake, determine the typical failure modes of the magnetorheological fluid brake and the failures of each component; 1.2: Based on the fault types of each component of the magnetorheological fluid brake, determine the cause, severity level, and repair method of each component fault of the magnetorheological fluid brake; Step 2: Based on the analysis results of the failure modes and hazards of the magnetorheological fluid brake, a dynamic fault tree is established, and the dynamic fault tree is modularly decomposed into a dynamic fault subtree module and a static fault subtree module. 2.1: Based on the analysis results of the impact and hazard of the failure modes of magnetorheological fluid brakes, a dynamic fault tree for magnetorheological fluid brakes is constructed, with the failure of the magnetorheological fluid brake as the top event, the three brake failure modes and the failures of the nine subsystems as intermediate events, and the failures of each component as the bottom events. 2.2: The dynamic fault tree is modularized by using a linear search method, decomposing it into independent dynamic fault subtree modules and static fault subtree modules; Step 3: Based on small sample data, obtain the upper and lower extreme values of the failure rates of each component of the magnetorheological fluid brake, construct interval models of the failure rates of each bottom event, and convert the interval models into high-dimensional ellipsoidal models using the minimum volume enclosing ellipsoid modeling method, thereby constructing ellipsoidal models of the top events of each failure subtree: ； in: For an n-dimensional ellipsoidal model, For ellipsoidal variables, Centered at the ellipsoid For the characteristic matrix, It is the set of n-dimensional real numbers; Step 4: Use the BDD method and Markov chains to perform qualitative and quantitative analysis and solve the dynamic fault tree; 4.1: Convert the dynamic fault subtree module into a Markov chain, and substitute the ellipsoid model constructed in step 3 into the solution formula of the Markov chain to obtain the failure rate of the top event of the dynamic fault subtree. ； In the formula: The transition rate from the normal state "0" to the failure state "Fa" is given. , The transition rate from the normal state "0" to the non-failure state "NF". , This represents the failure rate of the top event T of a chain of length n after a working time t. 4.2: Solving for the remaining static fault subtree using BDD; 4.3: The solution results of each dynamic fault subtree and static fault subtree are used as the base events of the new fault tree. The new fault tree is solved, and finally the failure probability of the top event is obtained.
2. The reliability analysis method for a magnetorheological fluid brake based on an ellipsoidal model according to claim 1, characterized in that: The three brake failure modes in step 2.1 are brake failure, brake release failure, and brake performance degradation.
3. The reliability analysis method for a magnetorheological fluid brake based on an ellipsoidal model according to claim 1, characterized in that: The top event is brake failure; the intermediate events are brake failure, brake release failure, decreased braking performance, brake disc failure, magnetic circuit failure, magnetorheological fluid degradation, magnetorheological fluid leakage, decreased magnetic induction intensity, brake disc failure, excitation coil failure, sealing ring failure, and excitation coil failure; the bottom event is drive shaft breakage, bracket damage, bearing jamming, uninterrupted power supply to the excitation coil, brake disc jamming, decreased brake disc friction, magnetorheological fluid loss, key damage, magnetic circuit control failure, magnetorheological fluid aging, excessively high braking temperature, excessively large magnetorheological fluid gap, contaminated magnetorheological fluid, end cap damage, bolt damage, demagnetization of the brake disc drive shaft, brake disc I failure, brake disc II failure, coil I failure, coil II failure, coil III failure, excessive load, normal aging, coil I failure, coil II failure, and coil III failure.
4. The reliability analysis method for a magnetorheological fluid brake based on an ellipsoidal model according to claim 1, characterized in that: For large equipment that lacks data, has unclear fault data, or cannot undergo reliability testing, the fault data of its components and systems can be obtained by taking the maximum and minimum values of the distribution range of the bottom events through component testing. This yields the interval model of the occurrence of the bottom events, and the ellipsoidal model of the top events can be obtained through the failure logic relationship between different bottom events.