A belief function-based reliability analysis method for wheel drive

Abstract

The present application relates to the field of reliability analysis calculation, more particularly to a wheel drive device reliability analysis method based on belief function, which is used to solve the problem of wheel drive device reliability analysis based on failure risk assessment under the condition of multi-source data fusion and cognitive uncertainty, and adopts the following scheme, that is, the failure probability and failure consequence reliability interval of each component are determined by the belief function method, the information of different independent evidence sources can be effectively fused, and the reliability analysis can be carried out under the condition that the existing data is insufficient; through the failure risk assessment of each component of the wheel drive device, the reliability analysis can be carried out by comprehensively considering the failure probability and failure consequence, the problem that the reliability analysis only considers the failure probability and the evaluation standard is single and difficult to apply to engineering practice is avoided, and the direction for the regulation and control of the reliability of subsequent components is provided.

Description

Technical Field

[0001] This invention relates to the field of reliability analysis and calculation, and more specifically to a reliability analysis method for wheel drive devices based on belief functions. Background Technology

[0002] Wind tunnel testing is crucial in vehicle aerodynamics development, and ground effect simulation is the first problem to be solved in wind tunnel testing. Compared with traditional fixed-floor systems, the five-belt system commonly used in current vehicle wind tunnels significantly improves the simulation quality of ground effects in wind tunnel tests. The five-belt system consists of a narrow central belt and four wheel drive units, among which the wheel drive units are responsible for driving the wheels to rotate and simulating the ground flow field in front of and behind the wheels, and are the core subsystem of the five-belt system.

[0003] Current reliability analyses of wheel drive systems are primarily based on probability theory, requiring the determination of fault distribution types before predicting failure times. Furthermore, they often focus only on failure probabilities, making it difficult to accurately identify actual high-risk components. In actual wind tunnel testing, reliability analyses of wheel drive systems often face challenges such as insufficient effective fault data, unclear direction and degree of component reliability control, and inconsistencies between data sources. Summary of the Invention

[0004] This invention provides a reliability analysis method for wheel drive devices based on belief functions, aiming to solve the reliability analysis problem of wheel drive devices under multi-source data fusion and cognitive uncertainty.

[0005] The above objectives are achieved through the following technical solutions:

[0006] A reliability analysis method for wheel drive systems based on belief functions includes the following steps:

[0007] Step 1: Define the data source and construct a framework and basic probability allocation for the failure probability and consequences of each component of the wheel drive device.

[0008] Specifically, basic probability allocations m1 and m2 are constructed based on historical failure data of the wheel drive unit in vehicle wind tunnel tests and corresponding manual evaluation information; basic probability allocations m3 and m4 are constructed based on failure cost data of the wheel drive unit in vehicle wind tunnel tests and corresponding manual evaluation information.

[0009] Step 2: Data fusion. M1 and M2 are merged together to obtain a new basic probability distribution, denoted as M5. M3 and M4 are merged together to obtain a new basic probability distribution, denoted as M6. Calculate and determine the confidence interval of the failure probability and failure consequences of each component.

[0010] Step 3: Calculate the risk of each component, classify the failure probability and failure consequences, and then draw a two-dimensional risk diagram;

[0011] Step 4: Analyze and assess the risks of each component.

[0012] Failure consequences are the costs resulting from component failure, including one or more of the following: production loss costs, environmental cleanup costs, medical costs, insurance costs, legal costs, costs of mobilizing emergency resources, and business loss costs due to reputational damage and reduced customer confidence.

[0013] The framework for failure probability is denoted as Θ, including low failure rates (denoted as L), medium failure rates (denoted as M), and high failure rates (denoted as H). Then:

[0014] Θ = {L, M, H};

[0015] The framework for failure consequences includes minor failure consequences denoted as l, moderate failure consequences denoted as m, and severe failure consequences denoted as h, then:

[0016] Θ = {l, m, h};

[0017] The basic probability assignment m is a mapping from a subset of frame Θ to [0,1], satisfying the following condition:

[0018]

[0019] The data fusion method is as follows:

[0020]

[0021] Where K is the conflict coefficient, defined as:

[0022]

[0023] Then there is

[0024] K1=m1(L)*m2(M)+m1(L)*m2(H)+m1(L)*m2(M,H)+m1(M)*m2(L+m1(M)*m2(H)+m1(M)*m2(L,H)+ m1(H)*m2(L)+m1(H*m2(M)+m1(H)*m2(L,M)+m1(L,M)*m2(H)+m1(L,H)*m2(M)+m1(M,H)*m2(L)

[0025] K2=m3(l)*m4(m)+m3(l)*m4(h)+m3(l)*m4(m,h)+m3(m)*m4(l)+m3(m)*m4(h)+m3(m)*m4(l,h)+ m3(h)*m4(l)+m3(h)*m4(m)+m3(h)*m4(l,m)+m3(l,m)*m4(h)+m3(l,h)*m4(m)+m3(m,h)*m4(l)

[0026]

[0027] Similarly

[0028]

[0029]

[0030] The method for calculating the confidence interval is as follows:

[0031] [Belief function bel, likelihood function pl]

[0032] The belief function bel is a mapping from a subset of frame Θ to [0,1], satisfying the following condition:

[0033]

[0034] bel(Θ)=1

[0035] The method for calculating the belief function of each subset of the failure probability is as follows:

[0036] bel(L)=m(L)

[0037] bel(M) = m(M)

[0038] bel(H)=m(H)

[0039] bel(L,M)=m(L)+m(M)+m(L,M)

[0040] bel(L,H)=m(L)+m(H)+m(L,H)

[0041] bel(M,H)=m(M)+m(H)+m(M,H)

[0042] bel(L,M,H)=m(L)+m(M)+m(H)+m(L,M)+m(L,H)+m(M,H)+m(L,M,H)=1;

[0043] The calculation method for the belief functions of each subset of failure consequences is the same as above;

[0044] The likelihood function pl is a mapping from a subset of frame Θ to [0,1], satisfying the following condition:

[0045]

[0046] pl(Θ)=1

[0047] The method for calculating the likelihood function of each subset of the failure probability is as follows:

[0048] pl(L)=m(L)+m(L,M)+m(L,H)+m(L,M,H)

[0049] pl(M)=m(M)+m(L,M)+m(M,H)+m(L,M,H)

[0050] pl(H)=m(H)+m(L,H)+m(M,H)+m(L,M,H)

[0051] pl(L,M)=m(L)+m(M)+m(L,M)+m(L,H)+m(M,H)+m(L,M,H)

[0052] pl(L,H)=m(L)+m(H)+m(L,M)+m(L,H)+m(M,H)+m(L,M,H)

[0053] pl(M,H)=m(M)+m(H)+m(L,M)+m(L,H)+m(M,H)+m(L,M,H)

[0054] pl(L,M,H)=m(L)+m(M)+m(H)+m(L,M)+m(L,H)+m(M,H)+m(L,M,H)=1;

[0055] The calculation method for the likelihood function of each subset of failure consequences is the same as above.

[0056] The method for determining the confidence interval is as follows: select the interval with the highest probability outside the entire set, that is, the interval with the highest mean of the corresponding belief function bel and likelihood function pl.

[0057] The method for calculating the risk of each component is as follows:

[0058] R i =P×C;

[0059] Among them, R i P represents the failure risk of the component; C represents the failure probability of the component; and C represents the failure consequence of the component.

[0060] The method for drawing the two-dimensional risk diagram is as follows: the x-axis represents the failure consequences, with a value range of [0,1], and the y-axis represents the failure probability, also with a value range of [0,1]. The diagram is then divided into four parts: low risk, medium risk, high risk, and extremely high risk, and high-risk and extremely high-risk components are identified.

[0061] The method for analyzing and evaluating the risks of each component is as follows: mark the failure risk of each component on a two-dimensional risk map, observe the area where it is located, if it is in a high-risk or extremely high-risk area, it is necessary to reduce its failure risk by improving its reliability. For components whose failure risk cannot be reduced by reducing reliability, the failure risk is reduced by reducing the consequences of failure, so that each component is in a medium- or low-risk area.

[0062] The reliability is defined as follows:

[0063] R(t) = P(T>t) = 1 - P(T≤t);

[0064] Where R(t) is the component reliability at time t; T is the component failure time;

[0065] The principle of reducing risk by improving reliability is as follows:

[0066]

[0067] Among them, R i (t) represents the component failure risk at time t.

[0068] The beneficial effects of the reliability analysis method for wheel drive devices based on belief functions of this invention are as follows:

[0069] The belief function method was used to determine the failure probability and the confidence range of failure consequences for each component. This method can effectively integrate information from different independent evidence sources and can perform reliability analysis when existing data is insufficient. By assessing the failure risk of each component of the wheel drive device, the reliability analysis can comprehensively consider both failure probability and failure consequences. This avoids the problem that conventional reliability analysis only considers failure probability, has a single evaluation standard, and is difficult to apply to engineering practice. This provides direction for the subsequent control of the reliability of each component. Attached Figure Description

[0070] Figure 1 This is a flowchart of a reliability analysis method for wheel drive devices based on belief functions;

[0071] Figure 2 It is a two-dimensional risk diagram;

[0072] Figure 3 This is a schematic diagram of the air bearing risk reduction process. Detailed Implementation

[0073] Combination Figure 1 A reliability analysis method for wheel drive devices based on belief functions includes the following steps:

[0074] Step 1: Define the data sources and construct a framework and basic probability allocation for the failure probability and consequences of each component, namely the drive roller, driven roller, moving belt, air bearing, sensor, drive shaft system, main drive motor, support bearing housing, hydraulic cylinder, adjustable bearing housing, deep groove ball bearing, connecting base, and simulated bump edge.

[0075] The data sources include: historical failure data and failure cost data of wheel drive units in vehicle wind tunnel tests, and ambiguous information formed by expert evaluation;

[0076] Among them, the failure probability is the probability of failure of each component of the wheel drive device;

[0077] Among these, the consequences of failure are the costs incurred due to component failure, such as the cost of production loss, the cost of cleaning up the polluted environment, medical costs, insurance costs, legal costs, the cost of mobilizing emergency resources, and the cost of business losses due to reputational damage and reduced customer confidence.

[0078] Here, the frame is denoted as Θ, which is a finite set of propositions containing all possible assumptions. In this embodiment, the frame of failure probability contains three elements: low failure rate denoted as L, medium failure rate denoted as M, and high failure rate denoted as H. Then:

[0079] Θ = {L, M, H};

[0080] Furthermore, Θ contains eight subsets. {L}, {M}, {H}, {L,M}, {L,H}, M,H}, {L,M,H}.

[0081] The framework for failure consequences also includes three elements: minor failure consequences are denoted as l, moderate failure consequences as m, and severe failure consequences as h. Therefore:

[0082] Θ = {l, m, h};

[0083] Furthermore, it contains eight subsets. {l}, {m}, {h}, {l,m}, {l,h}, {m,h}, {l,m,h}.

[0084] The basic probability assignment m is a mapping from a subset of frame Θ to [0,1], satisfying the following condition:

[0085]

[0086] The basic probability assignment construction methods include:

[0087] The method for constructing the basic probability allocation of failure probability is to construct the corresponding basic probability allocations m1 and m2 based on the historical failure data of the wheel drive device in the vehicle wind tunnel test and expert opinions.

[0088] The method for constructing the basic probability allocation of failure consequences involves constructing corresponding basic probability allocations m3 and m4 based on the failure cost data of the wheel drive device in vehicle wind tunnel tests and expert opinions.

[0089] Step 2: Data fusion, calculate and determine the confidence interval of the failure probability and failure consequences of each component; the confidence interval, also known as the uncertainty band, represents the range of possible probabilities. The narrower the uncertainty band, the more accurate the confidence interval.

[0090] The data fusion process involves: combining two independent basic probability assignments m1 and m2 from historical failure data of wheel drive units in vehicle wind tunnel tests and expert opinions to obtain a new basic probability assignment m5; and combining two independent basic probability assignments m3 and m4 from failure cost data of wheel drive units in vehicle wind tunnel tests and expert opinions to obtain a new basic probability assignment m6.

[0091] The data fusion method is as follows:

[0092]

[0093] Where K is the conflict coefficient, defined as:

[0094]

[0095] Then there is

[0096] K1=m1(L)*m2(M)+m1(L)*m2(H)+m1(L)*m2(M,H)+m1(M)*m2(L)+m1(M)*m2(H)+m1(M)*m2(L,H)+ m1(H)*m2(L)+m1(H)*m2(M)+m1(H)*m2(L,M)+m1(L,M)*m2(H)+m1(L,H)*m2(M)+m1(M,H)*m2(L)

[0097] K2=m3(l)*m4(m)+m3(l)*m4(h)+m3(l)*m4(m,h)+m3(m)*m4(l)+m3(m)*m4(h)+m3(m)*m4(l,h)+ m3(h)*m4(l)+m3(h)*m4(m)+m3(h)*m4(l,m)+m3(l,m)*m4(h)+m3(l,h)*m4(m)+m3(m,h)*m4(l)

[0098]

[0099] Similarly, we can obtain

[0100]

[0101]

[0102] The wheel drive device in the five-belt system includes many components such as drive roller, driven roller, movable belt, air bearing, strain gauge sensor, etc. For ease of explanation, the air bearing is used as an example, which is only a part of the embodiments of the present invention, and not all of the embodiments.

[0103] Assume the basic probability distributions m5 and m6 of the air bearings obtained after fusion are as follows:

[0104]

[0105] The method for calculating the confidence interval is as follows:

[0106] [Belief function bel, likelihood function pl]

[0107] The belief function bel is a mapping from a subset of frame Θ to [0,1], satisfying the following condition:

[0108]

[0109] bel(Θ)=1

[0110] Then there is

[0111] bel(L)=m5(L)=0.1

[0112] bel(M) = m5(M) = 0.2

[0113] bel(H)=m5(H)=0.3

[0114] bel(L,M)=m5(L)+m5(M)+m5(L,M)=0.3

[0115] bel(L,H)=m5(L)+m5(H)+m5(L,H)=0.4

[0116] bel(M,H)=m5(M)+m5(H)+m5(M,H)=0.9

[0117] bel(L,M,H)=m5(L)+m5(M)+m5(H)+m5(L,M)+m5(L,H)+m5(M,H)+m5(L,M,H)=1.

[0118] The likelihood function pl is a mapping from a subset of frame Θ to [0,1], satisfying the following condition:

[0119]

[0120] pl(Θ)=1

[0121] Then there is

[0122] pl(L)=m5(L)+m5(L,M)+m5(L,H)+m5(L,M,H)=0.1

[0123] pl(M)=m5(M)+m5(L,M)+m5(M,H)+m5(L,M,H)=0.6

[0124] pl(H)=m5(H)+m5(L,H)+m5(M,H)+m5(L,M,H)=0.7

[0125] pl(L,M)=m5(L)+m5(M)+m5(L,M)+m5(L,H)+m5(M,H)+m5(L,M,H)=0.7

[0126] pl(L,H)=m5(L)+m5(H)+m5(L,M)+m5(L,H)+m5(M,H)+m5(L,M,H)=0.8

[0127] pl(M,H)=m5(M)+m5(H)+m5(L,M)+m5(L,H)+m5(M,H)+m5(L,M,H)=0.9

[0128] pl(L,M,H)=m5(L)+m5(M)+m5(H)+m5(L,M)+m5(L,H)+m5(M,H)+m5(L,M,H)=1

[0129] In summary

[0130]

[0131]

[0132] The method for determining the confidence interval is as follows: select the interval with the highest probability outside the entire set, that is, the interval with the largest mean of the corresponding belief function bel and likelihood function pl. Clearly, the confidence interval for the air bearing failure probability is determined as follows.

[0133] {M,H}

[0134] Similarly, we can obtain

[0135]

[0136] Obviously, the confidence interval for the consequences of air bearing failure is determined as follows:

[0137] {m,h}

[0138] Step 3: Calculate the risk of each component, classify the failure probability and failure consequences, and then draw a two-dimensional risk diagram;

[0139] The method for calculating the risk of each component is as follows:

[0140] R i =P×C

[0141] Among them, R i P represents the failure risk of the component; C represents the failure probability of the component; and C represents the failure consequence of the component. Due to cognitive uncertainty, the obtained failure probability and failure consequence of the air bearing are both within a confidence range and cannot be directly multiplied. It is necessary to observe the failure risk in a two-dimensional risk diagram.

[0142] The failure probability classification method is as follows: {L} = [0, 0.2], {L, M} = [0.2, 0.4], {M} = {L, H} = [0.4, 0.6], {M, H} = [0.6, 0.8], {H} = [0.8, 1], then the failure probability classification of the air bearing is [0.6, 0.8].

[0143] The classification method for the failure consequences is as follows: {l} = [0, 0.2], {l, m} = [0.2, 0.4], {m} = {l, h} = [0.4, 0.6], {m, h} = [0.6, 0.8], {h} = [0.8, 1]. Therefore, the classification of the failure consequences of the air bearing is also [0.6, 0.8].

[0144] The method for drawing the two-dimensional risk diagram is as follows: the x-axis represents the failure consequence, with a value range of [0,1], and the y-axis represents the failure probability, also with a value range of [0,1]. The diagram is then divided into four parts: low risk, medium risk, high risk, and extremely high risk, occupying areas of 0.16, 0.28, 0.28, and 0.28 respectively. Figure 2 As shown.

[0145] Step 4: Analyze and assess the risks of each component, identify high-risk and extremely high-risk components, and reduce the risks by improving their reliability, so that all components are in the medium- or low-risk range.

[0146] The method for analyzing and assessing the risks of each component is as follows: The failure risk of each component is marked on a two-dimensional risk map. The location of each component is observed. If it is in a high-risk or extremely high-risk area, its failure risk needs to be reduced by improving its reliability. For components whose failure risk cannot be reduced by decreasing reliability, the failure consequences are reduced to lower the failure risk, ultimately ensuring that all components are in medium- or low-risk areas. Air bearings are located in a high-risk area, such as... Figure 3 As shown.

[0147] The reliability is defined as follows:

[0148] R(t) = P(T>t) = 1 - P(T≤t)

[0149] Where R(t) is the component reliability at time t; and T is the component failure time.

[0150] The principle of reducing risk by improving reliability is as follows:

[0151]

[0152] Among them, R i Let R(t) be the component failure risk at time t. Then, assuming the failure consequence C remains constant, the greater the reliability R(t), the greater the failure risk R. i The smaller (t) is, the lower the failure probability of the air bearing can be. Therefore, the failure risk can be reduced to the medium-risk range by improving reliability. Figure 3 As shown.

Claims

1. A reliability analysis method for wheel drive devices based on belief functions, characterized in that, Includes the following steps: Step 1: Define the data source and construct a framework and basic probability allocation for the failure probability and consequences of each component in the wheel drive system. Specifically, basic probability allocations m1 and m2 are constructed based on historical failure data of the wheel drive unit in vehicle wind tunnel tests and corresponding manual evaluation information; basic probability allocations m3 and m4 are constructed based on failure cost data of the wheel drive unit in vehicle wind tunnel tests and corresponding manual evaluation information. Step 2: Data fusion. M1 and M2 are merged together to obtain a new basic probability distribution, denoted as M5. M3 and M4 are merged together to obtain a new basic probability distribution, denoted as M6. Calculate and determine the confidence interval of the failure probability and failure consequences of each component. Step 3: Calculate the risk of each component, classify the failure probability and failure consequences, and then draw a two-dimensional risk diagram; Step 4: Analyze and assess the risks of each component.

2. The reliability analysis method for wheel drive devices based on belief functions according to claim 1, characterized in that, Failure consequences are the costs resulting from component failure, including one or more of the following: production loss costs, environmental cleanup costs, medical costs, insurance costs, legal costs, costs of mobilizing emergency resources, and business loss costs due to reputational damage and reduced customer confidence.

3. The reliability analysis method for wheel drive devices based on belief functions according to claim 1, characterized in that, The framework for failure probability is denoted as Θ, including low failure rates (denoted as L), medium failure rates (denoted as M), and high failure rates (denoted as H). Then: Θ = {L, M, H}; The framework for failure consequences includes minor failure consequences denoted as l, moderate failure consequences denoted as m, and severe failure consequences denoted as h, then: Θ = {l, m, h}; The basic probability assignment m is a mapping from a subset of frame Θ to [0,1], satisfying the following condition:

4. The reliability analysis method for wheel drive devices based on belief functions according to claim 1, wherein the data fusion method is as follows: in, K is the conflict coefficient, defined as: Then there is K1=m1(L)*m2(M)+m1(L)*m2(H)+m1(L)*m2(M,H)+m1(M)*m2(L)+m1(M)*m2(H)+m1(M)*m2(L,H)+ m1(H)*m2(L)+m1(H)*m2(M)+m1(H)*m2(L,M)+m1(L,M)*m2(H)+m1(L,H)*m2(M)+m1(M,H)*m2(L) K2=m3(l)*m4(m)+m3(l)*m4(h)+m3(l)*m4(m,h)+m3(m)*m4(l)+m3(m)*m4(h)+m3(m)*m4(l,h)+ m3(h)*m4(l)+m3(h)*m4(m)+m3(h)*m4(l,m)+m3(l,m)*m4(h)+m3(l,h)*m4(m)+m3(m,h)*m4(l) Similarly 5. The reliability analysis method for wheel drive devices based on belief functions according to claim 4, wherein the confidence interval calculation method is as follows: [Belief function bel, likelihood function pl] The belief function bel is a mapping from a subset of frame Θ to [0,1], satisfying the following condition: bel(Θ)=1 The belief function for each subset of the failure probability is calculated as bel(l) = m5(L). bel(M) = m5(M) bel(H) = m5(H) bel(L,M)=m5(L)+m5(M)+m5(L,M) bel(L,H)=m5(L)+m5(H)+m5(L,H) bel(M,H)=m5(M)+m5(H)+m5(M,H) bel(L,M,H)=m5(L)+m5(M)+m5(H)+m5(L,M)+m5(L,H)+m5(M,H)+m5(L,M,H)=1; The calculation method for the belief functions of each subset of failure consequences is the same as above; The likelihood function pl is a mapping from a subset of frame Θ to [0,1], satisfying the following condition: pl(Θ)=1 The likelihood function of each subset of the failure probability is calculated as follows: pl(L) = m5(L) + m5(L,M) + m5(L,H) + m5(L,M,H) pl(M)=m5(M)+m5(L,M)+m5(M,H)+m5(L,M,H) pl(H)=m5(H)+m5(L,H)+m5(M,H)+m5(L,M,H) pl(L,M)=m5(L)+m5(M)+m5(L,M)+m5(l,H)+m5(M,H)+m5(l,M,H) pl(L,H)=m5(L)+m5(H)+m5(L,M)+m5(L,H)+m5(M,H)+m5(L,M,H) pl(M,H)=m5(M)+m5(H)+m5(L,M)+m5(L,H)+m5(M,H)+m5(L,M,H) pl(L,M,H)=m5(L)+m5(M)+m5(H)+m5(L,M)+m5(L,H)+m5(M,H)+m5(L,M,H)=1; The calculation method for the likelihood function of each subset of failure consequences is the same as above.

6. The reliability analysis method for wheel drive device based on belief function according to any one of claims 1 to 5, wherein the method for determining the confidence interval is: selecting the interval with the highest probability outside the entire set, that is, the interval with the largest mean of the corresponding belief function bel and likelihood function pl.

7. The reliability analysis method for wheel drive devices based on belief functions according to claim 1, wherein the calculation method for the risk of each component is as follows: R i =P×C; in, R i P represents the failure risk of the component; C represents the failure probability of the component; and C represents the failure consequence of the component.

8. The reliability analysis method for wheel drive device based on belief function according to claim 1, wherein the failure probability classification method is: {L}=[0,0.2], {L,M}=[0.2,0.4], {M}={L,H}=[0.4,0.6], {M,H}=[0.6,0.8], {H}=[0.8,1]; The classification method for the failure consequences is as follows: {l} = [0, 0.2], {l, m} = [0.2, 0.4], {m} = {l, h} = [0.4, 0.6], {m, h} = [0.6, 0.8], {h} = [0.8, 1].

9. The reliability analysis method for wheel drive device based on belief function according to claim 1, wherein the method for drawing the two-dimensional risk diagram is as follows: the x-axis represents the failure consequence, with a value range of [0,1], and the y-axis represents the failure probability, also with a value range of [0,1]. The diagram is then divided into four parts: low risk, medium risk, high risk, and extremely high risk, and high-risk and extremely high-risk components are identified.

10. The reliability analysis method for wheel drive device based on belief function according to claim 9 reduces risk by improving reliability, ultimately ensuring that all components are in the medium- or low-risk range.

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