Switched reluctance motor reliability evaluation method considering repair rate

Abstract

This invention discloses a dimension-reduction reliability assessment method for switched reluctance motors (SRMs) that considers repairability. This method analyzes the faults of the SRM at structural levels, comprehensively converting the failure probabilities of each underlying component into overall system state transition parameters. Based on this, the repairability rate is calculated according to the actual periodic maintenance cycle of the equipment, and a Markov state transition equation system containing maintenance recovery paths is established. To avoid complex calculus operations involving high-order matrices, this invention utilizes Laplace transform to convert the dynamic process into algebraic calculations in the complex frequency domain, achieving analytical order reduction of the model. By performing algebraic analysis on the complex frequency domain function, the dynamic reliability function and mean time between failures (MTBF) of the system are directly obtained. This invention overcomes the shortcomings of traditional models, such as cumbersome computation and unrealistic lifespan predictions. While effectively reducing the computational complexity of microcontrollers, it significantly improves the accuracy of lifespan prediction for motor drive systems and enhances their engineering application value.

Description

Technical Field

[0003] This invention proposes a dimension-reduced reliability assessment method for switched reluctance motors that considers repair rate. This method comprehensively considers the outstanding fault-tolerant characteristics of the switched reluctance motor itself, as well as the actual repairability of the system under fault-tolerant degradation state. It also effectively reduces the solution dimension of the traditional Markov state equation through complex frequency domain analytical transformation, thereby significantly improving the accuracy and computational efficiency of drive system lifetime prediction. Background Technology

[0005] With the deepening of electrification in modern industry and transportation, highly reliable and efficient electric drive systems have become core supports for aerospace, new energy vehicles, and high-end equipment manufacturing. In the pursuit of ultimate safety and stable operation, the research and application of various special motors are receiving increasing attention. Among them, switched reluctance motors, with their absence of permanent magnets in both stator and rotor, extremely robust and durable structure, low manufacturing cost, and inherent phase-to-phase physical and electromagnetic isolation characteristics, exhibit excellent fault-tolerant operation potential. Therefore, they are highly favored in many complex application scenarios with stringent safety requirements, demonstrating extremely high engineering adaptability and commercial value.

[0006] Within a switched reluctance motor system, the coordinated operation of the power conversion topology and sensor network enables excellent fault isolation and fault-tolerant control capabilities, laying the foundation for derating operation of the motor after localized damage. For systems with dynamic state transition characteristics, using Markov models for reliability analysis has become a recognized and effective method in both academia and engineering.

[0007] However, existing dynamic reliability assessment models still face insurmountable technical bottlenecks in practical applications. On the one hand, the high-dimensional matrix differentiation operations of traditional Markov models result in excessive computational complexity, leading to extremely slow lifetime prediction processes and making it difficult to implement online real-time calculations and early warnings in the underlying microcontrollers. On the other hand, existing models generally treat system degradation as a unidirectional irreversible process, completely ignoring the crucial repairability characteristics in actual engineering. This significant deviation between the assessment model and actual equipment maintenance conditions not only leads to overly conservative results in metrics such as Mean Time To Failure (MTTF), but also weakens the scientific guiding value of reliability assessment for system periodic maintenance planning. Summary of the Invention

[0009] To address the shortcomings of existing technologies, this invention provides a method for dimensionality-reduction reliability assessment of switched reluctance motors that considers repair rate.

[0010] This invention first systematically elucidates the state aggregation mechanism of switched reluctance motors under multi-dimensional fault modes. This mechanism, through in-depth analysis of the failure rate of underlying components, accurately divides the complex system operating state into normal operating state and fault-tolerant degradation state, thus solidifying the data foundation for system reliability assessment from the physical level.

[0011] Building upon this foundation, this invention innovatively proposes a dimension-reduced Markov solution architecture that integrates repairability. This architecture calculates the correlation coefficients of the Markov state transition differential equations based on the underlying correlation failure rate and completely replaces the traditional high-order state transition matrix differential operations with complex frequency domain algebraic equations. Compared to traditional methods for solving high-dimensional state transition matrices, this dimension reduction method effectively avoids the common state space explosion problem in Markov models, significantly reducing computational complexity while maintaining the simplicity and intuitiveness of the theoretical derivation.

[0012] Finally, by analyzing the reduced-dimensional complex frequency domain function, the system's time-domain dynamic reliability and mean time to failure were accurately calculated. This evaluation system comprehensively considers the actual repairability of the system under fault-tolerant degradation conditions and achieves quantitative analysis of the system-level dynamic lifetime. This significantly reduces the computational burden on the microcontroller while comprehensively improving the accuracy and engineering practicality of switched reluctance motor reliability assessment. Attached Figure Description

[0014] Figure 1 This is the Markov state transition diagram of the switched reluctance motor of the present invention.

[0015] Figure 2 This is the Markov state transition diagram of the switched reluctance motor detection unit of the present invention.

[0016] Figure 3 This is the Markov state transition diagram of the power converter of the present invention.

[0017] Figure 4 This is a reliability block diagram model of the switched reluctance motor system of the present invention.

[0018] Figure 5 This is the reliability curve under the traditional static reliability block diagram model of this invention.

[0019] Figure 6 This is the reliability curve of the Markov model with repairability introduced in this invention. Detailed Implementation

[0021] The following description, in conjunction with the accompanying drawings, provides further examples of the invention.

[0022] This invention first establishes a continuous-time Markov model describing the dynamic derating and maintenance process of a switched reluctance motor system. The system is defined as having normal operating states and fault-tolerant degradation states. Based on the transition logic between system states, the Markov state transition differential equations of the system are constructed as follows:

[0023]

[0024] In the formula, P0(t) is the probability that the system is in a fault-free normal operating state at time t, X(t) is the probability that the system enters a derating fault-tolerant degradation state after a partial fault occurs at time t, and λ T The derating base failure rate for the system transitioning from normal operation to a fault-tolerant degradation state. The equivalent failure rate is the rate at which a secondary fault occurs in the fault-tolerant degradation state, leading to complete failure. μ is the recoverability rate of the system from the fault-tolerant degradation state or the complete failure state to the normal state through online intervention, regular maintenance, or shutdown maintenance.

[0025] To address the problem of excessive computational cost in solving complex matrices using traditional Markov models, this invention innovatively introduces a dimensionality reduction strategy based on algebraic simplification in the complex frequency domain. The system is initially assumed to be in a fully healthy state, i.e., the initial conditions are P0(0)=1 and X(0)=0. A Laplace transform is applied to the above differential equations, transforming the time-domain differential solution process into algebraic operations in the complex frequency domain, resulting in the following algebraic equation system:

[0026]

[0027] By simplifying and calculating this system of equations, the probability function P0(s) of the switched reluctance motor maintaining normal operation in the complex frequency domain can be accurately calculated:

[0028]

[0029] This leads to the degenerate state probability function X(s) in the complex frequency domain:

[0030]

[0031] The dynamic reliability of a system is the sum of the probabilities of the system being in normal operation and in a fault-tolerant degradation state. Therefore, the reliability dimension reduction analytical model R(s) in the complex frequency domain is derived as follows:

[0032]

[0033] Furthermore, traditional methods require solving an infinite integral over the time-domain curve to determine the mean time between failures (MTBF) of a system, a process that is extremely tedious and time-consuming. This invention utilizes the final value theorem of the Laplace transform to directly transform the solution of the infinite integral into a limit calculation in the complex frequency domain, greatly simplifying the computational steps.

[0034]

[0035] To accurately obtain system-level state transition rate parameters, this invention abandons the traditional static logic block diagram and uses a Markov process to specifically divide the switched reluctance motor drive system into three core modules: the switched reluctance motor itself, the detection unit, and the power converter, and establishes a low-level Markov state transition model for each module. The system is configured so that all modules start from the normal state (NS) and eventually evolve into the failure state (FS).

[0036] To clearly define the specific fault types of the above three major modules and their transition parameters in the Markov model, this invention systematically sorts out the underlying fault modes, as shown in Table 1:

[0037] Table 1 Failure Modes

[0038]

[0039] Based on the fault definitions in Table 1 above, the Markov state transition process for each module is as follows: The first part is the fault analysis of the motor's own module. For example... Figure 1 As shown, starting from the normal state, when an open circuit fault occurs, the motor has a failure rate λ. OW Transition to degenerate state A1; when a short-circuit fault occurs, the failure rate λ is used. SW The system transitions to the degenerate state A2. Due to the strong fault tolerance of the switched reluctance motor, the probability of a direct transition from the normal state to the failure state is extremely low (i.e., direct failure transition λ≈0 in the diagram). When in the degenerate state A1 or A2, if the corresponding fault occurs again, the system transitions to the failure state. The second part is the fault analysis of the detection unit module. For example... Figure 2 As shown, when the current sensor experiences a gain output failure, the system can maintain operation through a fault-tolerant algorithm, with a failure rate λ. GCS The system transitions to a degraded state B1; however, in the event of a fatal fault such as an open circuit or short circuit in the position sensor, or zero or constant output from the current sensor, the system directly transitions to a failed state. If the system is already in degraded state B1, a subsequent fatal fault will also transition it to a failed state. The third part is the power converter module fault analysis. For example... Figure 3 As shown, when the power converter experiences capacitor open-circuit and upper / lower MOSFET open-circuit or short-circuit faults, the system can switch to degraded operation by isolating the faulty phase, with corresponding fault rates λ.OC , λ OUM , λ SUM , λ OLM , λ SLM The system transitions to degraded states C1, C2, C3, C4, and C5. Capacitor short circuits and diode-related faults are directly fatal, causing the system to fail at a combined failure rate λ2. As each degraded state worsens, it transitions to a failure state at its corresponding failure rate (λ3 to λ7).

[0040] Based on actual engineering calibration or reliability manuals (such as MIL-HDBK-217F), the basic failure rate data of each underlying component is extracted, as shown in Table 2:

[0041] Table 2 Device Failure Rate

[0042]

[0043] λ in the table OW It is the failure rate of open-circuit faults in motor windings, λ SW It is the failure rate of short-circuit faults in motor windings, λ OPS It is the failure rate of open-circuit faults in position sensors, λ SPS It is the failure rate of position sensor short circuit failure, λ ZCS The failure rate of the current sensor with zero output, λ GCS The failure rate of the current sensor gain output, λ CCS The failure rate of the current sensor with a constant output value, λ OC It is the failure rate of capacitor open-circuit faults, λ SC It is the failure rate of capacitor short-circuit faults, λ OUM It is the failure rate of MOSFET open-circuit faults, λ SUM It is the failure rate of MOSFET short-circuit faults, λ OLM It is the failure rate of MOSFET open-circuit faults, λ SLM It is the failure rate of MOSFET short-circuit faults, λ OUD It is the failure rate of diode open-circuit faults, λ SUD It is the failure rate of the upper diode short-circuit fault, λ OLD It is the failure rate of diode open-circuit faults, λ SLD This is the failure rate of the diode short circuit fault.

[0044] Based on the aforementioned hierarchical Markov model, this invention performs equivalent fitting on the complex degradation and failure paths at the bottom level of each module, and obtains the state transition parameters required to construct the system-level differential equation.

[0045] λ TThis represents the equivalent transition rate of the system from a normal state to a fault-tolerant degradation state (i.e., states A1, A2, B1, and C1~C5 in the diagram). It is calculated by summing the fault-tolerant failure rates of the three main modules mentioned above:

[0046]

[0047] λ fatal This represents the probability that the system transitions directly from the normal state (NS) to the failure state (FS). Figure 1 , Figure 2 and Figure 3 (The sum of the directly connected branches λ, λ1, and λ2 in the equation).

[0048]

[0049] When the system is already in a degraded state, such as phase loss or derating, the backup fault tolerance capability of the entire drive system will decrease sharply. Based on the overall fault tolerance superposition characteristics of the system, the equivalent failure rate in the degraded state... It is approximately the sum of the fault-tolerant failure rate and the direct failure rate:

[0050]

[0051] While dynamic reliability models can accurately describe the fault-tolerant operating mode after a system failure, they assume that once a system enters a degraded state, it will remain in that state until final failure without any maintenance or recovery. However, in practical engineering, some temporary or localized failures can be eliminated through self-reset of the system's underlying code, hardware-level fault-tolerant switching, or rapid manual maintenance, allowing the system to switch back from a degraded state to normal operation. To make the theoretical calculations more consistent with actual engineering maintenance conditions, this invention innovatively introduces a repairability parameter to extend the traditional Markov state transition model. Repairability is an important parameter in reliability engineering describing how quickly a system recovers from a faulty state to normal operation, usually denoted as μ, and its physical meaning is the probability of completing a repair per unit time, measured in times per hour. Referring to the practical engineering experience of major overhauls every two years in wind power generation or industrial drive fields, this invention calculates the equivalent repairability μ of the system by converting this baseline maintenance cycle into hours, as follows:

[0052]

[0053] Traditional methods inevitably involve complex calculus calculations when solving high-dimensional state transition matrices. To avoid this computational challenge, this invention directly substitutes the core parameters obtained from the above equation into the Laplace complex frequency domain model, thereby transforming the originally complex matrix derivation into a simple algebraic equation for solution. To simplify the algebraic expression, let the system's overall attenuation constant A = λ. T +μ+ The calculation yields:

[0054]

[0055] Let the constant term in the denominator be B = λ T The calculation yields:

[0056]

[0057] Substituting the above-mentioned synthesis constants into the complex frequency domain reliability function R(s) derived from formula (5), we obtain the fully parameterized complex frequency domain algebraic equation:

[0058]

[0059] To obtain the reliability decay curve in the time domain, an inverse Laplace transform of R(s) is required. First, the complex frequency domain characteristic equation is solved. The two eigenvalues ​​r1 and r2:

[0060]

[0061] Substituting the data, we can obtain two eigenvalues ​​r1 and r2 as shown below:

[0062]

[0063]

[0064] Solving for the undetermined coefficients c1 and c2 of a double exponential function using the residue method:

[0065]

[0066]

[0067] By using the inverse Laplace transform, the partial fractions are converted into time-domain expressions, thereby constructing a dynamic reliability analytical model that has low computational burden and can be directly and efficiently run by the microcontroller.

[0068]

[0069] Traditional methods for calculating MTTF require definite integrals over [0,∞] of complex time-domain exponential functions. This invention leverages the computational advantages of the Laplace transform, directly applying the final value theorem and setting the complex frequency domain variable s→0, thus transforming the tedious calculus process into a simple algebraic division:

[0070]

[0071] Substituting the values ​​of A and B, the mean time between failures (MTBF) of the system after incorporating the repair rate is calculated (in hours):

[0072]

[0073] The calculation results show that the MTTF of up to 214,000 hours fully demonstrates the positive effect of introducing the repairability rate μ on the system lifespan. The theoretical prediction of the model is highly consistent with the actual maintenance situation in engineering.

[0074] To fully highlight the advancement and accuracy of the dynamic evaluation model of this invention, a traditional static reliability block diagram (RBD) model is introduced as a benchmark. For example... Figure 4 As shown, in the traditional RBD static model, the switched reluctance motor drive system is equivalent to a simple series system, consisting of the motor itself, the detection unit, and the power converter connected in series. The underlying logic of this model is set so that if any submodule fails, the system immediately enters a complete failure state.

[0075] In this series structure, the static total failure rate of the system is equal to the direct linear superposition of the total failure rates of the three modules, and its value is exactly equal to the equivalent failure rate of the system in the degradation state calculated in the previous steps of this invention. Therefore, based on the principle of reliability product in series systems, the traditional static reliability function R2(t) is derived:

[0076]

[0077] Based on this static function, by performing an infinite integral over the time axis, the mean time between failures (MTBF) of the system under the traditional RBD model is calculated:

[0078]

[0079] After completing the parameterization solution of the two models mentioned above, a visual comparative analysis is performed on the dynamic Markov reliability R1(t) with repair rate introduced in this invention and the traditional static reliability R2(t), as shown below. Figure 5 and Figure 6 As shown.

[0080] Figure 5 Static RBD model curve characteristics: This curve strictly follows the standard single exponential decay characteristic. Because the theoretical model does not incorporate fault tolerance and maintenance mechanisms, the system reliability drops sharply in the initial stages of operation. This precipitous drop fails to reflect the objective fact that equipment in actual engineering has a derating buffer period. Figure 6 The Markov model curve characteristic of this invention is that the double exponential decay curve derived based on Laplace order reduction exhibits a smoother transition characteristic. In the early stages of equipment operation, the curve shows a clear high-reliability maintenance plateau. This characteristic accurately reflects the actual physical process by which the system, when encountering a local fault, can rely on its own redundancy fault-tolerant mechanism to operate at reduced capacity and wait for periodic repair μ intervention, thereby effectively slowing down the rate at which overall reliability approaches the failure threshold.

[0081] Calculation and comparison results show that traditional reliability block diagram models, lacking consideration of fault tolerance and maintenance mechanisms, often lead to conservative and unrealistic lifespan assessments. This invention proposes a dimension-reduced reliability assessment method for switched reluctance motors that considers the repair rate. This method not only effectively alleviates the computational burden caused by high-order state transition matrices through algebraic transformations in the complex frequency domain, but also fully integrates the equipment's repair rate μ at the theoretical level. Compared to traditional methods, this invention significantly improves the accuracy of system dynamic lifespan prediction and provides a scientific and rigorous quantitative basis for intelligent health early warning and periodic maintenance planning throughout the entire lifecycle of the drive system.

Claims

1. To address the problems of complex high-dimensional matrix operations in existing dynamic reliability assessment models and the deviation of lifespan predictions from reality due to neglecting equipment maintenance characteristics, this invention proposes a dimension-reduced reliability assessment method for switched reluctance motors that considers the repairability rate. This method combines the fault-tolerant characteristics of switched reluctance motors with the actual repairability rate, and simplifies the solution of the Markov process through complex frequency domain transformation, thereby improving the accuracy and computational efficiency of lifespan prediction. The specific implementation includes the following steps: Step 1: Establish a continuous-time Markov model describing the dynamic derating and maintenance process of the switched reluctance motor system. Assume the system includes normal operating states and fault-tolerant degradation states, and construct the system's state transition differential equations: In the formula, P0(t) is the probability that the system is in a fault-free normal operating state, X(t) is the probability that the system enters a derating fault-tolerant degradation state, and λ T To reduce the basic failure rate, The equivalent failure rate of the degraded state is given by μ, and the repairability rate is given by μ. Step 2: Perform Laplace transform on both sides of the above differential equation system to transform the differential solution process in the time domain into algebraic operations in the complex frequency domain, and derive the analytical reliability model in the complex frequency domain: In the formula, R(s) is the reliability function in the complex frequency domain, and s is a complex variable in the complex frequency domain; Step 3: Using a Markov process, the switched reluctance motor drive system is decomposed into three core modules: the motor itself, the detection unit, and the power converter. A low-level state transition model is then established for each module. The complex degradation and failure paths at the low level of each module are equivalently fitted to derive the derating base failure rate λ in the equations described in Step 1. T Equivalent failure rate to degenerate state ; Step 4: Based on the actual preventive maintenance cycle of the equipment (two years), convert the time base to an hourly system and calculate the equivalent repairability of the system: ; Step 5: Substitute the core constants calculated in Steps 3 and 4 into the complex frequency domain analytical model derived in Step 2 for algebraic solution. Perform inverse Laplace transform on the partial fractions to obtain the time-domain dynamic reliability mathematical analytical model, thereby completing the comprehensive reliability assessment of the entire drive system.

2. The method for dimensionality reduction reliability assessment of a switched reluctance motor considering repair rate according to claim 1, characterized in that, Of the three core modules described in step 3, the motor module involves open-circuit and short-circuit faults in the windings; the detection unit module involves open-circuit, short-circuit, and abnormal output faults in the sensors; and the power converter module involves open-circuit and short-circuit faults in the capacitors, power switching transistors, and diodes.

3. The method for dimensionality reduction reliability assessment of a switched reluctance motor considering repair rate according to claim 1, characterized in that, A complex frequency domain solution method based on Laplace transform is adopted. This method replaces the traditional high-order state transition matrix differentiation operations with complex frequency domain algebraic equations, effectively reducing the computational complexity of the microprocessor and making the theoretical derivation process more rigorous and concise.

4. Building upon claim 3, and to address the shortcomings of reliability models that deviate from reality due to neglecting equipment maintenance, this invention innovatively introduces the concept of repairability to extend the traditional Markov state transition model. Compared to existing models that treat system degradation as a unidirectional irreversible process, this evaluation system comprehensively considers the actual repairability characteristics of the system under fault-tolerant degradation conditions, correcting the problem of overly conservative estimations of the system's mean time between failures (MTBF).

5. Based on claim 4, the present invention uses mean time to failure to describe the performance of reliability assessment. This index utilizes the final value theorem of the Laplace transform to transform infinite integrals into limit operations in the complex frequency domain. In the formula, MTTF is the mean time between failures (MTTF) of the entire switched reluctance motor drive system.

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