A method for evaluating real-time credibility of online RUL prediction results of a rotating machine

Abstract

The application provides a rotating machinery online RUL prediction result real-time credibility evaluation method, and belongs to the technical field of mechanical residual life evaluation; solves the problem of low calculation accuracy of existing evaluation indexes related to RUL prediction; comprises the following steps: acquiring real-time monitoring data representing the degradation of the rotating machinery; extracting features of the degradation state, and constructing a degradation index representing the health state of the rotating machinery; calculating the degradation increment in unit time; assuming the distribution type of the degradation increment in unit time, estimating the parameters of the degradation increment distribution in the random process RUL prediction model based on the maximum likelihood estimation method; calculating the probability distribution of the rotating machinery RUL prediction result based on the concept of first arrival time; when the RUL prediction model and result are determined, calculating the evaluation index affecting the credibility of the RUL prediction result, and calculating the evaluation index weight; using the membership function to fuzz the evaluation index; calculating the credibility of the RUL prediction result; and the application is applied to RUL prediction result evaluation.

Description

Technical Field

[0001] This invention provides a method for real-time reliability assessment of online RUL prediction results for rotating machinery, belonging to the field of mechanical remaining life assessment technology. Background Technology

[0002] In recent years, Remaining Useful Life (RUL) prediction technology has been widely used in the field of Prognostics and Health Management (PHM) for rotating machinery. This is because RUL prediction enables maintenance personnel to predict the occurrence of failures in advance, plan corresponding maintenance activities, prevent sudden equipment downtime, and thus improve equipment productivity and reduce operation and maintenance costs.

[0003] The Remaining Service Life (RUL) of rotating machinery is defined as the time span from any prediction point to the point of failure. Considering the combined effects of the machinery's own materials and the external environment, its degradation process is stochastic. To measure the impact of stochastic degradation in rotating machinery, the latest RUL prediction models tend to provide probabilistic RUL prediction results, that is, to describe the probability of different RUL durations using probability distributions. Current RUL prediction methods mainly include: RUL prediction based on physical failure models, data-driven RUL prediction, and hybrid models of both. Among them, the degradation data-driven RUL prediction method mainly utilizes sensors to collect health status parameters closely related to the remaining service life of the rotating machinery in real time (e.g., vibration, pressure, temperature, speed, etc.), then establishes a time-dependent model of the health status parameters, uses probability distributions to describe the uncertainty in RUL prediction, and thus achieves RUL prediction for the target equipment, with a wider range of applications.

[0004] The ultimate goal of RUL prediction results is to apply them to subsequent predictive maintenance decisions. Accurate RUL prediction results are crucial for these decisions, forming the foundation and prerequisite for the effectiveness of the formulated predictive maintenance strategy. However, due to the randomness of system degradation, RUL predictions always contain biases that are difficult to completely eliminate through technical means. Therefore, it is essential to evaluate the performance of RUL prediction results before or during the prediction process and before applying them to predictive maintenance decisions. Currently, the most widely used evaluation metric related to RUL prediction is undoubtedly prediction error. However, when RUL prediction results are in the form of a probability distribution, in addition to the issue of the overall distribution deviating from the true value, there are also concerns about the accuracy of the probability distribution describing prediction uncertainty. Furthermore, data-driven RUL prediction can be dynamically updated using online monitoring data, and the consistency of the prediction model and results also affects the practical application of the prediction results in subsequent predictive maintenance decisions; therefore, its impact cannot be ignored. In summary, comprehensively evaluating the real-time performance of online prediction results in the data-driven RUL prediction process from multiple dimensions to provide more comprehensive information for subsequent predictive maintenance decisions is one of the important issues that urgently needs to be addressed in the field of RUL prediction.

[0005] As mentioned earlier, current evaluation metrics related to RUL prediction are mostly constructed based on prediction error (the difference between the predicted value and the true value), requiring the actual RUL value to participate in the calculation. Their primary application scenario is comparing the model performance of different RUL prediction models based on the same offline dataset. However, when applying RUL prediction models in practice, the actual RUL of the target object cannot be known in advance during the prediction process; otherwise, the prediction would lose its meaning. This means that existing evaluation metrics related to RUL prediction cannot be calculated online. Whether from the perspective of different application scenarios or theoretical analysis, the performance of prediction models evaluated based on offline data cannot directly represent the performance of the output RUL prediction results when different input data are used. If the performance of RUL prediction results is not evaluated during the prediction process and they are directly used for subsequent predictive maintenance decision-making research, unpredictable decision biases can easily occur. Therefore, how to construct evaluation metrics and methods that can assess the real-time performance of RUL prediction results during the prediction process without relying on the actual RUL value is a pressing technical problem that needs to be solved in the practical application of online RUL prediction results for rotating machinery. Summary of the Invention

[0006] To address the problem that existing evaluation indicators related to RUL prediction require actual RUL values ​​for calculation, making them difficult to apply to real-world prediction scenarios and guide subsequent predictive maintenance decision-making research based on RUL prediction results, this invention proposes a real-time reliability evaluation method for online RUL prediction results of rotating machinery. It introduces a novel reliability evaluation index and calculation method to measure the performance of RUL prediction results in real time during the RUL prediction process.

[0007] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a method for real-time reliability assessment of online RUL prediction results for rotating machinery, comprising the following steps:

[0008] Step 1: Install various sensors on the rotating machinery to obtain real-time monitoring data characterizing its degradation;

[0009] Step 2: Extract features from the degradation state of rotating machinery and construct degradation indicators to characterize the health state of rotating machinery;

[0010] Step 3: Obtain the RUL prediction results for rotating machinery based on the stochastic process RUL prediction model, which specifically includes the following steps:

[0011] Step 3.1: Based on the degradation index characterizing the health status of rotating machinery constructed in Step 2, calculate the degradation increment per unit time;

[0012] Step 3.2: Assuming the distribution type of degradation increment per unit time, estimate the parameters of the degradation increment distribution in the stochastic process RUL prediction model based on the maximum likelihood estimation method;

[0013] Step 3.3: Calculate the probability distribution of the RUL prediction results for rotating machinery based on the concept of first arrival time;

[0014] Step 4, at any t n Once the RUL prediction model and RUL prediction results are determined, the evaluation indicators that affect the reliability of the RUL prediction results are calculated. These evaluation indicators include accuracy indicators, consistency indicators, and validity indicators.

[0015] Step 5: Calculate at t n The weights of evaluation indicators that affect the reliability of RUL prediction results at any given moment;

[0016] Step 6: Use the membership function to evaluate t n The evaluation metrics for each moment are blurred;

[0017] Step 7: Set the scores for RUL prediction results belonging to different confidence levels, and calculate t. n The reliability of the RUL prediction results at time 1.

[0018] In step 2, the mean square amplitude is specifically used to extract features of the degraded state of rotating machinery.

[0019] Step 3.3 calculates the rotating machinery t based on the concept of first arrival time. n The formula for the probability distribution of the RUL prediction result at time t is as follows:

[0020] rul n =inf{l n |X(t n +l n )≥D f};

[0021] In the above formula: D f The fault threshold is set in advance based on engineering experience; X(t) n +l n ) for the system at t n +l n The cumulative amount of degradation state at any given time.

[0022] The formula for calculating the accuracy index in step 4 is as follows:

[0023]

[0024] In the above formula: F n (Δx i Let π(Δx; a, b) be the fitted cumulative distribution function calculated from the degradation increment probability density function. This is the empirical cumulative distribution function obtained based on historical degradation incremental data without assuming a distribution type.

[0025] The formula for calculating the consistency index in step 4 is as follows:

[0026] ;

[0027] In the above formula: JS(·) is the Jensen-Shannon divergence, π n (Δx) is t n The probability density function of the degradation increment at time π n-1 (Δx) is t n-1 The probability density function of the degradation increment at time step 1.

[0028] The formula for calculating the validity index in step 4 is as follows:

[0029]

[0030] In the above formula: c is the regularization factor, f n (l n ) for t nThe probability density function of the RUL prediction result at time t.

[0031] Step 5 specifically includes the following steps:

[0032] Based on historical prediction time t i The calculated values ​​of the evaluation indicators (1≤i≤n) are denoted as the set of historical evaluation indicators.

[0033] Step 5.1: Calculate the ratio of the historical evaluation value of each evaluation indicator to the total evaluation value, that is, calculate the degree of variation of each indicator. The expression is as follows:

[0034]

[0035] Step 5.2, calculate at t n The information entropy of each evaluation indicator at time t is expressed as follows:

[0036]

[0037] Step 5.3, calculate at t n The information redundancy of each evaluation indicator at any given time is expressed as follows:

[0038]

[0039] Step 5.4, calculate at t n The weights of each evaluation indicator at each time point are expressed as follows:

[0040]

[0041] Step 5.5, obtain the result at t n The weight vector at time step is:

[0042]

[0043] Step 6 specifically includes the following steps:

[0044] Step 6.1: Divide the credibility into 5 levels v k (k = 1, 2, 3, 4, 5), and are respectively denoted as unreliable (v1), low reliability (v2), medium reliability (v3), high reliability (v4), and completely reliable (v5);

[0045] Step 6.2: Select the triangular membership function and calculate the membership values ​​of the above evaluation indicators belonging to different confidence intervals. The calculation formula is as follows:

[0046]

[0047] In the above formula: q k(·) indicates that a certain evaluation indicator belongs to different credibility evaluation levels. k membership degree The threshold for classifying credibility rating levels;

[0048] Get t n Fuzzy confidence evaluation matrix of RUL prediction results at time 1 Its expression is as follows:

[0049]

[0050] Step 7, the credibility calculation, includes the following steps:

[0051] Step 7.1, Calculate t n The confidence fuzzy vector of the RUL prediction result at time step is expressed as follows:

[0052]

[0053] In the above formula:

[0054] Step 7.2: Set the scores of the RUL prediction results belonging to different confidence levels as S = [s1, s2, s3, s4, s5], and calculate the confidence level of the RUL prediction results. The expression is as follows:

[0055] Cr n =Fv n *S T =fv1*s1+fv2*s2+fv3*s3+fv4*s4+fv5*s5.

[0056] The advantages of this invention compared to existing technologies are as follows: Considering the application scenarios of RUL prediction results, this invention defines a new evaluation index—reliability—to measure the performance of RUL prediction results. This method proposes three secondary evaluation factors affecting the reliability of RUL prediction results: accuracy, consistency, and validity. This method establishes calculation models for accuracy, consistency, and validity that can be calculated in real-time during the prediction process. This method utilizes the entropy weight method to achieve dynamic updates of the weights of secondary evaluation factors. This method employs a fuzzy comprehensive evaluation method to integrate the accuracy, consistency, and validity evaluation factors, thereby realizing the reliability calculation of RUL prediction results. This reliability evaluation method is simple and clear in form, efficient and convenient in calculation, and can provide reliability simultaneously with RUL prediction, filling the gap in the current RUL prediction process where there is a lack of real-time performance evaluation of RUL prediction results. Attached Figure Description

[0057] The present invention will be further described below with reference to the accompanying drawings:

[0058] Figure 1 Flowchart of the real-time reliability assessment method for online RUL prediction results of rotating machinery provided in this embodiment of the invention;

[0059] Figure 2 A schematic diagram of the triangular membership function provided in an embodiment of the present invention;

[0060] Figure 3 The rotating machinery sensor monitoring data and the degradation trajectory after RMS feature extraction provided in the embodiments of the present invention are used to characterize the health status of the rotating machinery.

[0061] Figure 4 The degradation increment distribution map provided by the embodiments of the present invention using different candidate models;

[0062] Figure 5 The probability density function curves of RUL prediction results obtained at different prediction times are provided in the embodiments of the present invention.

[0063] Figure 6 The graph shows the membership and confidence results obtained based on the proposed confidence method at different prediction times in the embodiments of the present invention. Detailed Implementation

[0064] like Figures 1 to 6 As shown, this invention provides a method for real-time reliability assessment of online RUL prediction results for rotating machinery, mainly including the following steps:

[0065] Step 1: Install various sensors on the rotating machinery to acquire real-time monitoring data characterizing its degradation;

[0066] An acceleration sensor is installed in the bearing housing of the main test chamber, a temperature sensor is installed inside the gearbox, and a noise sensor is installed directly above the main test chamber.

[0067] Step 2: Extract features from the degradation state of rotating machinery and construct degradation indices that characterize the health status of rotating machinery;

[0068] Feature extraction of the degradation state of rotating machinery is performed using mean square magnitude, at any t n At time t, the mean square amplitude of the time series of a discrete random signal can be expressed as:

[0069]

[0070] In the above formula: k is the number of sampling points, n = F s ×t n F s Let x(t) be the sampling frequency. i () represents historical sample values.

[0071] Step 3: Obtain RUL prediction results for rotating machinery based on the stochastic process RUL prediction model;

[0072] The general form of a stochastic process prediction model is:

[0073] X(t+τ)=x(t)+ΔX(τ), ΔX(τ)~π(Δx, a(τ), b(τ)) (2);

[0074] In the formula, x(t) is the system state at time t, ΔX(τ) is the cumulative amount of degradation state of the system in τ unit time intervals, which may follow a gamma distribution, normal distribution, inverse Gaussian distribution, etc. depending on the specific form of the degradation increment data π(·), while a(τ) and b(τ) represent the model drift parameter and diffusion parameter related to the time interval length τ, respectively.

[0075] Step 3.1: Based on the degradation index characterizing the health status of rotating machinery constructed in Step 2, calculate the degradation increment per unit time:

[0076] Δx(Δt i )=x(t i )-x(t i-1 (3);

[0077] Where, Δt i =t i -t i-1 .

[0078] Let Δt1 = Δt2 = ... = Δt n =Δt, that is, calculating the degradation increment of rotating machinery at equal intervals, the above formula can be simplified as:

[0079] Δx i =x(t) i )-x(t i-1 (4).

[0080] Step 3.2: When all degradation increments are calculated based on a unit time Δt, the probability density function of the degradation increment distribution can be denoted as π(Δx; a, b), where a is the shape parameter of the degradation increment distribution and b is the scale parameter of the shape parameter of the degradation increment distribution. Subsequently, based on any t... n The historical degradation increment set ΔX obtained at each moment n ={Δx1, Δx2, ..., Δx} n The parameters of the degradation increment distribution are estimated using the maximum likelihood estimation method.

[0081]

[0082] In the above formula: a n and bn They represent the values ​​at t n The shape and scale parameters of the degradation increment service distribution are dynamically updated based on the latest acquired state monitoring data.

[0083] Step 3.3: When the model parameters are determined, calculate t based on the concept of first arrival time. n The remaining lifetime of the time system n The probability density function:

[0084] rul n =inf{l n |X(t n +l n )≥D f} (6);

[0085] In the above formula: D f The fault threshold is usually set in advance based on engineering experience.

[0086] With ΔX~N(μ, σ) 2 For example, where μ is the drift parameter and σ is the diffusion parameter, the probability density function of the corresponding RUL prediction result can be obtained by the following formula:

[0087]

[0088] Step 4: At any t n Once the RUL prediction model and RUL prediction results are determined, the evaluation indicators affecting the reliability of the RUL prediction results are calculated.

[0089] Step 4.1: Accuracy metrics:

[0090]

[0091] In the above formula: F n (Δx i Let π(Δx; a, b) be the fitted cumulative distribution function. This is the empirical cumulative distribution function obtained based on historical degradation incremental data without assuming a distribution type.

[0092] Step 4.2: Consistency Indicators:

[0093] ;

[0094] Where JS(·) is the Jensen-Shannon divergence.

[0095] Step 4.3: Effectiveness Indicators:

[0096]

[0097] Where c is the regularization factor, f n (l n ) for t n The probability density function of the RUL prediction result at time t.

[0098] Step 5: Calculate at t n The weights of evaluation indicators that affect the reliability of RUL prediction results at any given moment;

[0099] Based on historical prediction time t i The calculated values ​​of the evaluation indicators (1≤i≤n) show that the set of historical calculated values ​​for different evaluation indicators is as follows:

[0100] Step 5.1: Calculate the ratio of the historical evaluation value of each evaluation indicator to the total evaluation value, that is, calculate the degree of variation of each indicator.

[0101]

[0102] Taking accuracy as an example, its calculation formula is as follows:

[0103]

[0104] Step 5.2: Calculate at t n The information entropy of each evaluation indicator at any given time is calculated using the following formula:

[0105]

[0106] Taking accuracy as an example, its historical evaluation value set The information entropy is as follows:

[0107]

[0108] Step 5.3: Calculate at t n The information redundancy of each evaluation indicator at any given time is calculated using the following formula:

[0109]

[0110] Taking accuracy as an example again, its expression is:

[0111]

[0112] Step 5.4: Calculate at t n Weights of each evaluation indicator at any given time:

[0113]

[0114] Step 5.5: At this point, we can obtain the result at t. n The weight vector at time step is:

[0115]

[0116] Step 6: Use membership functions to fuzzify the evaluation indicators;

[0117] Step 6.1: Divide the credibility into 5 levels v k (k = 1, 2, 3, 4, 5), and are respectively labeled as unreliable (v1), low reliability (v2), medium reliability (v3), high reliability (v4), and completely reliable (v5).

[0118] Step 6.2: Select the triangular membership function and calculate the membership values ​​of the above evaluation indicators belonging to different confidence intervals. The specific form is as follows:

[0119]

[0120] In the above formula: q k (·) represents a specific evaluation indicator belonging to the credibility evaluation level v. k membership degree This represents the threshold for classifying credibility rating levels.

[0121] Thus, we can obtain t n Fuzzy confidence evaluation matrix of RUL prediction results obtained at time step

[0122]

[0123] Step 7: Credibility Calculation

[0124] Step 7.1: Calculate t n The confidence fuzzy vector of the RUL prediction result at time step:

[0125] Step 7.1, Calculate t n The confidence fuzzy vector of the RUL prediction result at time step is expressed as follows:

[0126]

[0127] In the above formula:

[0128] Step 7.2: Set the scores of the RUL prediction results belonging to different confidence levels as S = [s1, s2, s3, s4, s5], and calculate the confidence level of the RUL prediction results. The expression is as follows:

[0129] Cr n =Fv n *ST =fv1*s1+fv2*s2+fv3*s3+fv4*s4+fv5*s5(19).

[0130] The above is based solely on t. n Taking a specific moment as an example, this paper explains the steps for evaluating the real-time reliability of online RUL prediction results. As the rotating machinery continues to operate, new monitoring data can be continuously acquired. By repeating the above steps, the RUL prediction model, RUL prediction results, and the reliability of the RUL prediction results can be dynamically updated.

[0131] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments;

[0132] The flowchart of the real-time reliability assessment method for online remaining life prediction results of rotating machinery is as follows: Figure 1 As shown, it includes the following steps:

[0133] Step 1: Perform condition monitoring on the degradation data of rotating machinery to obtain real-time monitoring data characterizing the degradation of rotating machinery:

[0134] The implementation case used a closed-loop power flow test bench for gear fatigue life testing. The center distance of the test bench was 150mm, and the motor speed was 1200r / min. Vibration of the gearbox, oil temperature, and noise were monitored during the test. Hardened gears made of alloy steel with a tooth surface hardness of 58-61HRC were used in the test, with a carburizing and quenching surface treatment. A staggered interlocking meshing method was adopted. The main test gear had a module m=3, number of teeth z1=z2=50, pressure angle α=20°, and tooth width 29mm (actual working tooth width 13-14mm); the auxiliary test gear had a number of teeth z3=z4=24, pressure angle α=20°, and working tooth width 20mm. Two gear meshing frequencies were used: 1000Hz for the main test gear and 480Hz for the auxiliary test gear. L-CKC320 industrial closed-loop gear oil was used for the test.

[0135] A total of 11 sensors were used in the experiment. Accelerometers were installed in the bearing housing of the main test chamber, temperature sensors were installed inside the gearbox, and noise sensors were installed directly above the main test chamber. Sensors 1-8 were accelerometers; sensors 1-4 were arranged radially on the bearing housing of the main test chamber, sensors 7 and 8 were arranged axially on the main test chamber, and sensors 5 and 6 were arranged radially on the bearing housing of the auxiliary test chamber. Sensors 9 and 10 were sound sensors, located approximately 40 cm above the main and auxiliary test chambers, respectively. Sensor 11 was a temperature sensor for measuring the lubricating oil temperature, located inside the main test chamber, and was used to measure the lubricating oil temperature during the experiment. The experiment used a conventional group method, i.e., constant load, with a torque of 822.7 Nm. A gear was considered faulty when a tooth broke during the test.

[0136] Step 2: Extract features from the degradation state of rotating machinery and construct degradation state indices:

[0137] In the life prediction, 200 sets of vibration signals output by sensor No. 4, which is closest to the broken tooth location and located in the bearing housing, were selected for feature extraction during the gear fatigue test. The sampling frequency was 25.6 kHz, and the sampling time was 60 seconds. The average value was taken as the sampling data at the current sampling moment. The sampling interval was 1 hour. By converting the number of sampling points into monitoring time, the curve of the feature value output by sensor No. 4 changing with the monitoring time could be obtained.

[0138] The overall trend of the mean square amplitude curve of sensor No. 4 reflects the relationship between the wear condition and vibration energy at each monitoring point of the test gear. This curve includes the mean square amplitude of the vibration signal from the initial break-in stage to the tooth breakage at 200 hours. The mean square amplitude y at the time of tooth breakage can be determined from the gear fatigue test. * (T * =672.7414, denoted as the degradation threshold.

[0139] Step 3: Establish an incremental model of the degradation state based on independent incremental processes;

[0140] Let x t Let be the degradation state value of the rotating machinery at time t. Using formula (4), calculate the difference between degradation state values ​​corresponding to the time intervals between adjacent times. Record the historical degradation states obtained before time t to calculate the historical degradation increment, and denote it as {Δx1, Δx2, ... Δx}. t}

[0141] Suppose {Δx1, Δx2, ..., Δx} t} follows a normal distribution N(μ, σ) 2 The model parameters are estimated using the maximum likelihood estimation method shown in formula (5), and the estimated parameter values ​​are denoted as (μ). t , σ t ).

[0142] The probability density function of the RUL prediction result is calculated based on formula (7).

[0143] While the rotating machinery is still operating normally, as the corresponding prediction time progresses and new monitoring data arrives, the corresponding degradation state data and corresponding degradation state increment data can be added. Steps 3.1-3.3 can then be performed to update the RUL prediction model and RUL prediction results.

[0144] To illustrate the dynamic update characteristics of degradation data-driven RUL prediction and its prediction result reliability evaluation method, the embodiments of this invention select a fixed time t. k=60, 70, ..., 190 Update model parameters and RUL prediction results, and conduct subsequent credibility assessment.

[0145] The corresponding results of the RUL prediction model at different times are shown in the figure. Figure 4 As can be seen, the model gradually stabilizes as the amount of incremental degradation data used for degradation modeling increases, which undoubtedly increases the consistency of the output RUL prediction results. RUL prediction results at different times are shown below. Figure 5 As can be seen, as the prediction time approaches the failure time, the expected value of the predicted RUL gradually approaches the actual RUL. Similarly, from... Figure 5 Furthermore, it can be observed that the probability density function of the RUL prediction results converges more closely as the time of failure approaches. In summary, the performance of data-driven RUL prediction results gradually improves with the increase of degraded data.

[0146] Step 4: Calculate the accuracy, consistency, and validity evaluation factors respectively;

[0147] The fitted cumulative distribution is calculated based on the estimated model parameters, and the empirical cumulative distribution is calculated based on the degradation increment data itself. The range of the degradation increment data Δx is set to -0.015 to 0.02, and the step size is 0.0001. The maximum difference between the fitted cumulative distribution and the empirical cumulative distribution when they take the same value is calculated using formula (8).

[0148] Based on the current t k The probability density function f of the degradation increment fitted at time t k (Δx) and based on t k-1 The probability density function f of the degradation increment fitted at time t k-1 (Δx), using the idea of ​​numerical integration, the range of Δx is set to -0.015-0.02, the differential operator is 0.0001, and the consistency evaluation value is calculated using formula (9);

[0149] Based on the calculated probability density function f of the current RUL prediction results k (l k The information entropy of ) is determined by using the concept of numerical integration, setting l k The value range is 0-300, the differential operator is 1, and its information entropy is calculated using formula (10), where the regularization factor is...

[0150] Step 5: Set the threshold value of the triangular membership function used for fuzzing the accuracy evaluation factor and the consistency evaluation factor to λ. A，1 =λ C，1 =0.5, λ A，2 =λ C，2 =0.75, λ A，3 =λ C，3=0.875, λ A，4 =λ C，4 =0.9375, λ A，5 =λ C，5 =0.96875; Set the threshold values ​​for the triangular membership functions used to fuzzify the validity evaluation factors to λ. E，1 =0.03125, λ E，2 =0.0.0625, λ E，3 =0.125, λ E，4 =0.25, λ E，5 =0.5, and the fuzzy evaluation matrix composed of the above three evaluation factors is calculated using formula (16).

[0151] Step 6: Based on the historical values ​​of each evaluation factor, calculate the weight vector composed of the corresponding weights using formulas (11) to (15).

[0152] Step 7: Based on the fuzzy evaluation matrix and weight vector calculated in Steps 5 and 6, calculate the credibility fuzzy vector using formula (18), setting s1 = 0, s2 = 0.25, s3 = 0.5, s0.75, s5 = 1, and calculate the credibility using formula (19). The corresponding results are shown in [the original text]. Figure 6 .

[0153] contrast Figure 5 and Figure 6 It is evident that as the amount of data increases, the expected value of the RUL prediction results gradually approaches the true value, while the fluctuations gradually decrease and the degree of convergence gradually increases. Under the combined influence of these three factors, the reliability of the RUL prediction results gradually increases.

[0154] The online RUL prediction result real-time reliability evaluation method proposed in this invention is not limited to RUL prediction of rotating machinery equipment, but can also be applied to RUL prediction problems of other electromechanical products. The RUL prediction method is not limited to the Wiener independent incremental process (assuming a normal distribution of degradation increments) used in the implementation case, and the determination of the weights of secondary indicators is not limited to the entropy weight method, nor is the fusion of secondary indicators limited to the fuzzy comprehensive evaluation method. Implementers can make appropriate adjustments to the RUL prediction method, weight determination method, and comprehensive evaluation method according to actual needs. Any adjustments and modifications made by implementers without departing from the concept of this invention should also be considered within the scope of protection of this invention.

[0155] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for real-time reliability assessment of online RUL prediction results for rotating machinery, characterized in that: Includes the following steps: Step 1: Install various sensors on the rotating machinery to obtain real-time monitoring data characterizing its degradation; Step 2: Extract features from the degradation state of rotating machinery and construct degradation indicators to characterize the health state of rotating machinery; Step 3: Obtain the RUL prediction results for rotating machinery based on the stochastic process RUL prediction model, which specifically includes the following steps: Step 3.1: Based on the degradation index characterizing the health status of rotating machinery constructed in Step 2, calculate the degradation increment per unit time; Step 3.2: Assuming the distribution type of degradation increment per unit time, estimate the parameters of the degradation increment distribution in the stochastic process RUL prediction model based on the maximum likelihood estimation method; Step 3.3: Calculate the probability distribution of the RUL prediction results for rotating machinery based on the first-arrival time concept; Step 3.3 calculates the probability distribution of the RUL prediction results for rotating machinery based on the first-arrival time concept. The formula for the probability distribution of the RUL prediction result at time t is as follows: ； In the above formula: The fault threshold is set in advance based on engineering experience; For the system in The cumulative amount of degradation state at any given time; Step 4, in any Once the RUL prediction model and RUL prediction results are determined, the evaluation indicators affecting the reliability of the RUL prediction results are calculated. These evaluation indicators include accuracy indicators, consistency indicators, and validity indicators. The formula for calculating the accuracy index in step 4 is as follows: ； In the above formula: The probability density function of the degradation increment Calculate the fitted cumulative distribution function. The shape parameter represents the distribution of the degradation increment. The shape parameter and scale parameter represent the distribution of the degradation increment. This is the empirical cumulative distribution function obtained based on historical degradation increment data without assuming a distribution type. The formula for calculating the consistency index in step 4 is as follows: ； In the above formula: For Jensen-Shannon divergence, for The probability density function of the degradation increment at time t. for The probability density function of the degradation increment at time step; The formula for calculating the validity index in step 4 is as follows: ； In the above formula: As a regularization factor, for The probability density function of the RUL prediction result at time t; Step 5, Calculate The weights of evaluation indicators that affect the reliability of RUL prediction results at any given moment; Step 6: Use membership functions to... The evaluation metrics for each moment are blurred; Step 7: Set the scores for RUL prediction results belonging to different confidence levels, and calculate... The reliability of the RUL prediction results at time 1.

2. The method for real-time reliability assessment of online RUL prediction results for rotating machinery according to claim 1, characterized in that: In step 2, the mean square amplitude is specifically used to extract features of the degraded state of rotating machinery.

3. The method for real-time reliability assessment of online RUL prediction results for rotating machinery according to claim 1, characterized in that: Step 5 specifically includes the following steps: Based on historical prediction time The calculated values ​​of the evaluation indicators are denoted as the historical evaluation indicator set. , , ; Step 5.1: Calculate the ratio of the historical evaluation value of each evaluation indicator to the total evaluation value, that is, calculate the degree of variation of each indicator. The expression is as follows: ； Step 5.2, Calculate in The information entropy of each evaluation indicator at time t is expressed as follows: ； Step 5.3, Calculate in The information redundancy of each evaluation indicator at any given time is expressed as follows: ； Step 5.4, Calculate The weights of each evaluation indicator at each time point are expressed as follows: ； Step 5.5, obtain in The weight vector at time step is: 。 4. The method for real-time reliability assessment of online RUL prediction results for rotating machinery according to claim 3, characterized in that: Step 6 specifically includes the following steps: Step 6.1: Divide the credibility into 5 levels. And in order, they are marked as unreliable. Low reliability Medium credibility Highly reliable Completely credible ; Step 6.2: Select the triangular membership function and calculate the membership values ​​of the above evaluation indicators belonging to different confidence intervals. The calculation formula is as follows: ； In the above formula: For a certain evaluation indicator to belong to different credibility evaluation levels membership degree The threshold for classifying credibility rating levels; get Fuzzy confidence evaluation matrix of RUL prediction results at time 1 Its expression is as follows: 。 5. The method for real-time reliability assessment of online RUL prediction results for rotating machinery according to claim 1, characterized in that: Step 7, the credibility calculation, includes the following steps: Step 7.1, Calculation The confidence fuzzy vector of the RUL prediction result at time step is expressed as follows: ； In the above formula: ; Step 7.2: Set the scores for RUL prediction results belonging to different confidence levels as follows. The confidence level of the RUL prediction result is calculated using the following expression: 。

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