Degradation equipment quantization process parameter feasible region analysis method under prediction performance constraint

Abstract

The invention provides a degraded equipment quantization process parameter feasible region analysis method under predictive performance constraint, which belongs to the technical field of reliability engineering, and comprises the following steps of: describing a quantization error caused by digital-to-analog conversion in a data transmission engineering by adopting a uniform quantizer; a random degradation process based on a Wiener process is constructed, and life prediction solving is realized; establishing a performance measurement criterion for measuring the difference between equipment life distribution and equipment estimated life distribution, and solving a feasible region of quantization parameters in an equipment degradation process under the condition of a given life prediction allowable range; aiming at equipment monitoring data which generally have measurement errors and quantization errors in an actual measurement process, the method effectively improves decision conservative property caused by directly using the monitoring data, ensures the precision of a life prediction result and a reliability evaluation result, provides a powerful theoretical basis for management decisions such as spare part ordering and optimal replacement of equipment, and has a good application prospect. And efficient and reasonable equipment management is realized.

Description

Technical Field

[0001] The invention belongs to the technical field of reliability engineering, and in particular relates to a feasible domain analysis method for quantitative process parameters of degraded equipment under prediction performance constraints. Background Art

[0002] In the industrial production process, the performance characteristics of equipment may decrease with the accumulation of operating time. When the performance degradation characteristics exceed the allowable range, failure will occur. If the fault can be discovered in time or the remaining useful life (RUL) can be accurately predicted in the early stage of performance degradation, and a scientific and reasonable health management strategy can be formulated, the failure may not occur, thus avoiding disruption to the normal operation of the equipment and increasing additional operation and maintenance costs. Therefore, accurately characterizing the equipment degradation process and predicting the remaining life are of great significance to ensure the safe and reliable operation of the system.

[0003] In the actual measurement process, due to the influence of interference, noise, and non-ideal instruments, there are random measurement errors in the sensor monitoring data, which hinder the fair and realistic description of the health status of the equipment. To address this problem, the prior art uses additive Gaussian distribution to accurately simulate random measurement errors. The prior art takes into account the influence of measurement errors and establishes a mixed effect degradation model based on the Wiener process. It also solves the uncertainty problem in RUL prediction caused by measurement errors, individual differences, and time-varying uncertainties. Nonlinear RUL prediction methods with measurement errors are also studied.

[0004] In engineering practice, analog-to-digital conversion (ADC) is widely used for discretization purposes in order to record continuous-time signals and transmit digital data. Due to the limited word length accuracy, the quantization error generated by ADC is inevitable. When the quantization step size is small enough, the effect of this error can be ignored for simplicity. However, in spacecraft, satellites, drones, etc., telemetry technology is usually used for signal acquisition and transmission. Due to the limited channel capacity, low cost, and large amount of data, there is a quantization error problem that cannot be ignored in data transmission. Taking satellite data transmission as an example, the telemetry data received on the ground often shows obvious quantization errors, which may lead to unacceptable estimation deviations if used directly for degradation modeling and RUL prediction. Therefore, prediction based on degraded data with quantization errors is a problem worth studying.

[0005] Monitoring data is the basic premise and basis for conducting data-driven rule prediction research. If the influence of sensor measurement errors and data quantization process can be effectively alleviated, the deviation of equipment RUL estimation will be significantly reduced, thereby providing strong theoretical support for subsequent maintenance decisions and minimizing personnel and property losses. Since measurement errors in degradation data are difficult to eliminate, it is a practical method to limit these errors to a reasonable range to ensure the accuracy of life prediction. The prior art first proposed and studied the feasible domain of measurement errors for given performance accuracy requirements in life prediction. This method achieves the performance requirements of life prediction by determining the feasible range of measurement errors. Considering that the measurement error is time-dependent, the prior art introduces a KL distance-based method to analyze the feasible domain of sensor measurement errors and further studies its impact on maintenance decisions. However, in addition to measurement errors, the quantization process errors caused by limited data transmission are also difficult to identify and estimate online, resulting in the inability to observe the actual degradation process. Therefore, how to design the feasible region of the step size of the quantization process to ensure that the life prediction results are within the allowable requirements has raised new challenges. Summary of the invention

[0006] In view of the above-mentioned deficiencies in the prior art, the present invention provides a method for analyzing the feasible domain of quantitative process parameters of degraded equipment under prediction performance constraints, which solves the problems that the feasible domain of quantitative process parameters of equipment degradation is difficult to accurately solve, the availability of monitoring data is poor, and the direct prediction results are seriously deviated from the actual situation.

[0007] In order to achieve the above objectives, the technical solution adopted by the present invention is: a feasible domain analysis method for quantitative process parameters of degraded equipment under prediction performance constraints, comprising the following steps:

[0008] S1. Based on the Wiener process, the equipment degradation process is constructed under the influence of measurement error. The uniform quantizer is used to describe the quantization error caused by the digital-to-analog conversion during the equipment data transmission process, and the equipment life prediction is solved. The estimated results of the equipment estimated life with measurement error and quantization error, and the expectation and variance of the equipment estimated life distribution are obtained respectively;

[0009] S2. Based on the expectation and variance of the equipment estimated life distribution, establish a performance metric to measure the difference between the equipment's true life distribution and the equipment's estimated life distribution;

[0010] S3. Given the allowable range conditions for life prediction, use the performance measurement criteria to solve the feasible domain of the quantization process parameters of the degraded equipment and complete the feasible domain analysis of the quantization process parameters of the degraded equipment.

[0011] The beneficial effects of the present invention are as follows: the present invention targets equipment monitoring data in which measurement errors and quantization errors are common in actual measurement processes, and under the constraints of life prediction performance, determines the feasible domain of the quantization process of equipment degradation to effectively improve the decision-making conservatism caused by directly using monitoring data, thereby achieving accurate solution of the feasible domain of the quantization process parameters of the degraded equipment and improving the availability of monitoring data.

[0012] Furthermore, the S1 comprises the following steps:

[0013] S101. Define the equipment life as the time when the degradation process exceeds the failure threshold for the first time, and construct a degradation process with measurement error based on the RUL estimation method of the Wiener process;

[0014] S102, according to the degradation process containing measurement error, a uniform quantizer is used to describe the quantization error caused by analog-to-digital conversion in the device data transmission project, which is defined as an observed degradation process, and the quantization process parameters include measurement error parameters and quantization error parameters, and the feasible domain of the measurement error parameters and the quantization error parameters is defined;

[0015] S103, constructing an actual observed degradation process according to the functional relationship between the observed degradation process and the degradation process containing measurement errors and the real degradation process of the equipment;

[0016] S104. Based on the actual observed degradation process, the PDF form corresponding to the estimated life of the equipment is derived using the total probability formula, and according to the properties of the truncated normal distribution, the PDF form corresponding to the transformed estimated life of the equipment is obtained, and the expectation and variance of the distribution of the estimated life of the equipment are calculated.

[0017] The beneficial effect of the above further scheme is: the present invention uses the RUL estimation method based on the Wiener process to accurately characterize and model the equipment degradation data, define the feasible domain of the equipment life and the quantization process, and combine the degradation process containing measurement errors and quantization errors, the degradation process containing measurement errors and the equipment degradation process to derive the estimated life of the equipment, which provides basic data support for the subsequent performance measurement criteria for measuring the difference between the equipment life distribution and the equipment estimated life distribution.

[0018] Furthermore, the expressions of the feasible domains of the measurement error parameters and the quantization error parameters are as follows:

[0019]

[0020] T=inf{t:X(t)≥ω|X(0)<ω}

[0021] T ε,e = inf{t:Y(t)≥ω|Y(0)<ω}

[0022]

[0023] in, represents the feasible domain of measurement error parameters and quantization error parameters of the degradation process, θ ε,e represents the model parameters, D(T ε,e ,T) represents the equipment life T and the estimated equipment life T with measurement error and quantization error ε,e The deviation function between max represents the maximum allowable life prediction deviation, T ε,e represents the estimated lifetime of the device with measurement error and quantization error, T represents the true lifetime of the device, inf{·} represents the infimum of the elements in the set, X(t) represents the true degradation process of the device, X(0) represents the initial degradation state of the device, t represents time, ω represents the failure threshold, Y(t) represents the observed degradation process, Y(0) represents the initial observed degradation state, qu(·) represents a nonlinear mapping function of a uniform quantizer, It represents the degradation process containing measurement error, ε(t) represents the measurement error corresponding to the device at time t, and e(t) represents the quantization error caused by the digital-to-analog conversion at time t.

[0024] Furthermore, the expression of the actual observed degradation process is as follows:

[0025]

[0026] in, represents a degradation process with measurement error, ε(t) represents the measurement error at time t and obeys Gaussian distribution μ ε and Both represent measurement error parameters, e t represents the quantization error caused by the digital-to-analog conversion at time t, and obeys the uniform distribution e t ~U(a,b), a and b are the upper and lower bound parameters of the uniform distribution, q is the quantization error parameter, and q=ba, X(t) is the actual degradation process of the equipment, X(0) is the initial degradation state of the equipment, Y(t) is the actual observed degradation process, λ is the individual characteristics of the degradation of the same batch of equipment, B(t) is the standard Brownian motion, σ B B(t) represents the diffusion term of the degradation process, σ B represents the diffusion coefficient of the degradation process;

[0027] Furthermore, the estimated life span of the device is T ε,e PDF format The expression is as follows:

[0028]

[0029] in, represents the initial measurement data with measurement error, y0 represents the initial monitoring data with quantization error, exp(·) represents the natural exponential function, Φ(·) represents the distribution function of the standard normal distribution, t represents time, ω represents the failure threshold, μ ε and Both represent measurement error parameters, and a and b represent the upper and lower bound parameters of the uniform distribution.

[0030] Furthermore, the estimated life span of the transformed equipment is T ε,e Corresponding PDF format The expression is as follows:

[0031]

[0032] Where y0 represents the initial monitoring data with quantization error, exp(·) represents the natural exponential function, Φ(·) represents the distribution function of the standard normal distribution, t represents time, ω represents the failure threshold, μ ε and Both represent measurement error parameters, and a and b represent the upper and lower bound parameters of the uniform distribution.

[0033] Furthermore, the S2 comprises the following steps:

[0034] S201. Based on the estimated results of the estimated life of the equipment, the expectation and variance of the estimated life of the equipment are used to characterize the difference between the actual life of the equipment and the estimated life of the equipment based on the relative increase rate of the coefficient of variation method; wherein the relative increase rate of the coefficient of variation R ξ (T ε,e ,T) is as follows:

[0035]

[0036] Among them, ξ(T ε,e ) represents the estimated life of the equipment T ε,e ξ(T) represents the coefficient of variation of the actual life of the equipment T;

[0037] S202. Based on the estimated result of the estimated life of the equipment, and the expectation and variance of the estimated life distribution of the equipment, define the relative increase rate of variance, and use the relative increase rate of the coefficient of variation and the relative increase rate of variance as performance measurement criteria for measuring the difference between the equipment life distribution and the estimated life distribution of the equipment; wherein the relative increase rate of variance R var (T ε,e ,T) is as follows:

[0038]

[0039] Among them, var(T ε,e ) represents the estimated life of the equipment T ε,e The variance of the distribution, var(T) represents the variance of the distribution of the true life of the equipment T.

[0040] The beneficial effect of the above further scheme is: the present invention adopts the relative increase rate of the coefficient of variation to characterize the degree of difference between the life and the estimated life of the equipment according to the uncertainty characteristics of the life prediction results, and defines the relative increase rate of the variance, thereby improving the accuracy of the predicted life.

[0041] Furthermore, the S3 comprises the following steps:

[0042] S301, given the life prediction allowable range conditions, combined with the relative increase rate of the variation coefficient, determine the feasible domain of the quantized process parameters under the relative increase rate of the variation coefficient;

[0043] S302. Given the allowable range conditions for life prediction, combined with the relative increase rate of variance, determine the feasible domain of the quantitative process parameters under the relative increase rate of variance, and complete the feasible domain analysis of the quantitative process parameters of the degraded equipment.

[0044] Furthermore, the measurement error parameter μ under the relative increase rate of the variation coefficient is ε and And the expression of the feasible domain of the quantization error parameter q is as follows:

[0045]

[0046] Among them, R ξ (T ε,e ,T) represents the relative increase rate of the coefficient of variation, ξ(T ε,e ) represents the estimated life of the equipment T ε,e The coefficient of variation of ξ(T) represents the coefficient of variation of equipment life T, D max represents the maximum allowable life prediction deviation, λ represents the individual characteristics of the degradation of the same batch of equipment, σ B represents the process parameter, ω represents the failure threshold, and y0 represents the initial monitoring data with quantization error.

[0047] Furthermore, the measurement error parameter μ under the relative increase rate of variance is ε and And the expression of the feasible domain of the quantization error parameter q is as follows:

[0048]

[0049] Among them, λ represents the individual characteristics of the degradation of the same batch of equipment, σ B represents the process parameter, ω represents the failure threshold, y0 represents the initial monitoring data with quantization error, υmin Relative rate of increase of variance R var (T ε,e ,T) lower limit,υ max Relative rate of increase of variance R var (T ε,e ,T)’s upper limit.

[0050] The beneficial effect of the above further scheme is: the present invention uses the relative increase rate of the coefficient of variation and the relative increase rate of the variance to accurately analyze the feasible domain of the quantitative process parameters of equipment degradation under the constraints of the life prediction performance, ensure the availability of the monitoring data, and avoid the direct prediction results from seriously deviating from the actual situation. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 The figure is a flow chart of the method of the present invention.

[0052] Figure 2 Figures #1 and #2 are temperature rise data of a certain type of control moment gyro in this embodiment.

[0053] Figure 3 Figures #3 and #4 are temperature rise data of a certain type of control moment gyro in this embodiment.

[0054] Figure 4 Figure 3 is the temperature rise data of a certain type of control moment gyro in this embodiment.

[0055] Figure 5 This is a graph showing the variation of life prediction deviation under different quantization error parameters in this embodiment.

[0056] Figure 6 2 is a lifespan PDF diagram under different quantization error parameters in this embodiment.

[0057] Figure 7 Graph showing the feasible domain of measurement error and quantization step length for different maximum allowable lifetime prediction deviations in this embodiment. DETAILED DESCRIPTION

[0058] The specific implementation modes of the present invention are described below so that those skilled in the art can understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific implementation modes. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations utilizing the concept of the present invention are protected.

[0059] Before describing this embodiment, the following terms are explained:

[0060] Wiener process: Wiener process (drift Brownian process);

[0061] RUL: Remaining Useful Life;

[0062] PDF: probability density function;

[0063] CDF: Cumulative distribution function;

[0064] SBM: Standard Brownian Motion.

[0065] Example

[0066] like Figure 1 As shown, the present invention provides a feasible domain analysis method for quantifying process parameters of degraded equipment under prediction performance constraints.

[0067] In this embodiment, the temperature rise data of a certain type of control moment gyro is used for example verification, and its degradation process is as follows: Figure 2 and Figure 3 As shown in Figure 1, the condition monitoring data exhibits rough and stepped characteristics due to obvious quantization errors, which is mainly attributed to the limitations of analog-to-digital conversion. It may lead to overestimation or underestimation of potential degradation states, thereby compromising the accuracy of RUL prediction. Therefore, it is impractical to directly use condition monitoring data with quantization errors to construct the degradation process and predict RUL. Due to the limited transmission channel, quantization errors are difficult to identify directly. In order to ensure accurate life prediction, the appropriate word length accuracy must be carefully selected from the analog-to-digital conversion, so as to effectively control the quantization error within a reasonable range.

[0068] In this embodiment, a feasible domain analysis method for predicting the quantitative process parameters of degraded equipment under performance constraints is implemented as follows:

[0069] S1. Based on the Wiener process, the equipment degradation process is constructed under the influence of measurement error. The uniform quantizer is used to describe the quantization error caused by the digital-to-analog conversion during the equipment data transmission process, and the equipment life prediction is solved. The estimated results of the equipment estimated life with measurement error and quantization error, the expectation and variance of the equipment estimated life distribution are obtained respectively. The implementation method is as follows:

[0070] S101. Define the equipment life as the time when the degradation process exceeds the failure threshold for the first time, and construct a degradation process with measurement error based on the RUL estimation method of the Wiener process;

[0071] S102, according to the degradation process containing measurement error, a uniform quantizer is used to describe the quantization error caused by analog-to-digital conversion in the device data transmission project, which is defined as an observed degradation process, and the quantization process parameters include measurement error parameters and quantization error parameters, and the feasible domain of the measurement error parameters and the quantization error parameters is defined;

[0072] S103, constructing an actual observed degradation process according to the functional relationship between the observed degradation process and the degradation process containing measurement errors and the real degradation process of the equipment;

[0073] S104. Based on the actual observed degradation process, the PDF form corresponding to the estimated life of the equipment is derived using the total probability formula, and according to the properties of the truncated normal distribution, the PDF form corresponding to the transformed estimated life of the equipment is obtained, and the expectation and variance of the distribution of the estimated life of the equipment are calculated.

[0074] In this embodiment, since the degradation data in actual engineering is usually non-monotonic and the Wiener process has good mathematical properties, this type of random process is often used to describe the situation where the degradation process of the system is a continuous fluctuation. Therefore, the present invention uses this type of random process to describe the random degradation process of the equipment {X(t), t≥0}.

[0075] In this embodiment, the RUL estimation method based on the Wiener process characterizes the equipment degradation data through the Wiener process model, and then estimates the equipment life based on the degradation process. Generally, X(t) is defined to represent the degradation process related to time t. The equipment life T is defined as the time when the degradation process X(t) first exceeds the failure threshold ω, and its expression is as follows:

[0076] T=inf{t:X(t)≥ω|X(0)<ω}

[0077] Where T represents the real life of the equipment, inf{·} represents the infimum of the elements in the set, X(t) represents the real degradation process of the equipment, X(0) represents the initial degradation state of the equipment, t represents time, and ω represents the failure threshold;

[0078] In engineering time, considering the influence of traditional measurement errors, the degradation data actually monitored cannot usually be directly considered as the true degradation state of the equipment. At this time, the degradation process actually observed contains measurement errors. The expression is as follows:

[0079]

[0080] Among them, ε(t) represents the measurement error corresponding to the device at time t. When the degradation process contains measurement error When transmitted via analog-to-digital conversion, the expression for observing the degradation process Y(t) is as follows:

[0081]

[0082] Where qu(·) represents the nonlinear mapping function of the uniform rounding quantizer. For better explanation, let the quantization error caused by the digital-to-analog conversion be

[0083] In this embodiment, the observed degradation process Y(t) includes quantization error and measurement error.

[0084] Furthermore, based on the concept of first arrival time, the expression for the estimated life of the equipment considering the influence of quantization error and measurement error is as follows:

[0085] T ε,e = inf{t:Y(t)≥ω|Y(0)<ω}

[0086] Among them, T ε,e In order to make the estimated life of the equipment close to the estimated value of the equipment life, the measurement error and quantization error must meet certain requirements, that is, according to the equipment life T and the estimated life of the equipment T ε,e The deviation between determines the feasible domain of measurement error. Therefore, the parameter range within the feasible domain of the quantization process of the present invention is The expression is as follows:

[0087]

[0088] in, represents the parameter range within the feasible domain of the quantization process, D max represents the maximum allowable life prediction deviation, θ ε,e Denotes the measurement error ε(t) and the quantization error e t The model parameters, D(T ε,e ,T) represents the equipment life T and the estimated equipment life T ε,e The deviation function between

[0089] In this embodiment, when the influence of the traditional measurement error and the quantization process are considered at the same time, the expression of the observed device degradation process {Y(t), t≥0} is as follows:

[0090]

[0091] in, represents a degradation process with measurement error, ε(t) represents the measurement error at time t and obeys Gaussian distribution μ ε and Both represent measurement error parameters, e t represents the quantization error caused by the digital-to-analog conversion at time t, and obeys the uniform distribution e t~U(a,b), a and b are the upper and lower bound parameters of the uniform distribution, q is the quantization error parameter, and q=ba, X(t) is the actual degradation process of the equipment, X(0) is the initial degradation state of the equipment, Y(t) is the observed degradation process, λ is the individual characteristics of the degradation of the same batch of equipment, B(t) is the standard Brownian motion SBM, σ B B(t) represents the diffusion term of the degradation process, σ B Represents process parameters; at this time, the estimated life of the equipment is T ε,e The corresponding PDF and CDF are and

[0092] According to the observed degradation process Y(t) and the degradation process with measurement error The functional relationship of the equipment degradation process X(t) can be used to construct the actual observed degradation process and e t ~U(a,b), using the total probability formula, the estimated life of the equipment under the action of the quantitative process T can be derived ε,e The PDF form of the expression is as follows:

[0093]

[0094] According to the properties of truncated normal distribution, the estimated life of the equipment is T ε,e The expression of the distribution transformation is as follows:

[0095]

[0096] Furthermore, the estimated life of the equipment is T ε,e The expected value E(T ε,e ) and variance var(T ε,e ) is as follows:

[0097]

[0098]

[0099] S2. Based on the expectation and variance of the estimated life distribution of the equipment, a performance metric is established to measure the difference between the actual life distribution of the equipment and the estimated life distribution of the equipment. The implementation method is as follows:

[0100] S201. Based on the estimated results of the estimated life of the equipment, the expectation and variance of the estimated life of the equipment are used to characterize the difference between the actual life of the equipment and the estimated life of the equipment based on the relative increase rate of the coefficient of variation method; wherein the relative increase rate of the coefficient of variation R ξ (T ε,e ,T) is as follows:

[0101]

[0102] Among them, ξ(T ε,e ) represents the estimated life of the equipment T ε,e ξ(T) represents the coefficient of variation of the actual life of the equipment T;

[0103] S202. Based on the estimated result of the estimated life of the equipment, and the expectation and variance of the estimated life distribution of the equipment, define the relative increase rate of variance, and use the relative increase rate of the coefficient of variation and the relative increase rate of variance as performance measurement criteria for measuring the difference between the equipment life distribution and the estimated life distribution of the equipment; wherein the relative increase rate of variance R var (T ε,e ,T) is as follows:

[0104]

[0105] Among them, var(T ε,e ) represents the estimated life of the equipment T ε,e The variance of the distribution, var(T) represents the variance of the distribution of the true life of the equipment T.

[0106] In this embodiment, the coefficient of variation is used to measure the degree of difference between random variables, reflecting the uncertainty characteristics of the life prediction results. The coefficient of variation represents the ratio of the absolute value of the standard deviation of the random variable to the mean, that is, the inverse of the signal-to-noise ratio. The expression of the coefficient of variation is as follows:

[0107]

[0108] Where Z represents the relevant distribution function; when the measurement error has little influence, the equipment life T and the estimated equipment life T ε,e The relative difference of the coefficient of variation of the distribution is relatively small. Therefore, in order to accurately measure the difference between the two, a method based on the relative increase rate of the coefficient of variation is proposed to accurately characterize the equipment life T and the estimated equipment life T ε,e The degree of difference, the relative increase rate of the coefficient of variation R ξ (T ε,e ,T) is smaller, indicating that the life predicted by the degradation process {Y(t), t≥0} is more accurate. When the measurement error and quantization error have little effect on the predicted life, the relative increase rate of the coefficient of variation R ξ (T ε,e ,T) should be less than a given value D max .

[0109] Define equipment life T and equipment estimated life T ε,e The relative increase rate of variance R var (T ε,e,T); Similarly, the relative increase rate of variance R var (T ε,e ,T) is smaller, indicating that the life predicted by the degradation process {Y(t), t≥0} is more accurate. When the measurement error and quantization error have little effect on the predicted life, the relative increase rate of variance R var (T ε,e ,T) should satisfy υ min ≤R var (T ε,e ,T)≤υ max Among them, υ max ≥υ min ≥0 is the upper and lower limits of the prediction variance.

[0110] In this embodiment, since the life prediction result is a random variable, it is difficult for traditional Mahalanobis distance, Euclidean distance, etc. to effectively measure the degree of deviation between random variables. KL divergence is used. KL divergence is an effective method for measuring the asymmetry of the difference between two probability distributions. Suppose two random variables P and Q, whose probability distribution density functions are f p(x) and f q(x) , the expression of the relative entropy D(P||Q) of random variables P and Q is as follows:

[0111]

[0112] In order to solve the asymmetric problem of KL divergence and ensure that the estimated life of the equipment T can be effectively measured ε,e The degree of deviation from the equipment life T. Here, KL distance is used for measurement, and KL distance D is usually defined KL The expression for (P||Q) is as follows:

[0113]

[0114] It can be seen that the KL distance D KL (P||Q) satisfies non-negativity and continuity, and also satisfies distance symmetry. In addition, if and only if the equipment lifetime T and the equipment estimated lifetime T ε,e When the probability distribution of is completely consistent, D KL (P||Q) = 0; when variables P and Q are far apart and have no overlap, the KL divergence value tends to infinity. If the maximum allowable life prediction deviation D is defined max , when D KL (T ε,e ||T)≤D max When the equipment life is estimated to be T ε,e The deviation from the equipment life T is within the allowable range, which can in turn indicate that the influence of the quantization error of the monitoring data on the accuracy of life prediction is within the allowable range.

[0115] In this embodiment, the KL distance is used to solve the KL divergence asymmetry problem, and effectively measure the degree to which the estimated life of the device deviates from the device life.

[0116] S3. Given the allowable range conditions for life prediction, using the performance measurement criteria, solve the feasible domain of the quantitative process parameters of the degraded equipment, and complete the feasible domain analysis of the quantitative process parameters of the degraded equipment. The implementation method is as follows:

[0117] S301, given the life prediction allowable range conditions, combined with the relative increase rate of the variation coefficient, determine the feasible domain of the quantized process parameters under the relative increase rate of the variation coefficient;

[0118] S302. Given the allowable range conditions for life prediction, combined with the relative increase rate of variance, determine the feasible domain of the quantitative process parameters under the relative increase rate of variance, and complete the feasible domain analysis of the quantitative process parameters of the degraded equipment.

[0119] In this embodiment, under the constraints of life prediction performance, it is necessary to comprehensively consider the influence of measurement error and quantization error and conduct feasible domain analysis of the quantization process. The present invention calculates the reasonable value range of measurement error and quantization error for the measurement data under the influence of the quantization process under the given life prediction allowable range conditions to ensure the normal operation of the equipment.

[0120] In this embodiment, 0≤R ξ (T ε,e ,T)≤D max , then

[0121] In the formula,

[0122]

[0123] Therefore, the expression of the relative increase rate range of the coefficient of variation is as follows:

[0124]

[0125] Through calculation, we can further obtain that given the prediction performance requirement 0≤R ξ (T ε,e ,T)≤D max , measurement error parameter μ ε and And the expression of the quantization error parameter q is as follows:

[0126]

[0127] From the above analysis, it can be seen that when the equipment monitoring data has both measurement error and quantization error, the known prediction performance requirement D max and process parameters λ and σ B, the measurement error parameter μ can be determined respectively ε and The feasible domain of the quantization error parameter q.

[0128] In this embodiment, based on the relative increase rate of variance R var (T ε,e ,T), to meet the given prediction performance requirementυ min ≤R var (T ε,e ,T)≤υ max , then the measurement error parameter μ ε and And the quantization error parameter q should satisfy the following conditions:

[0129]

[0130] It can be seen that when the equipment monitoring data has both measurement error and quantification error, the known prediction performance requirement is υ min ,υ max , process parameter λ and process parameter σ B , the measurement error parameter μ can be determined respectively ε and The feasible domain of the quantization error parameter q.

[0131] In this embodiment, according to the actual needs of the control torque gyro, the failure index is usually designed: the temperature rise of the high-speed shaft temperature relative to the environment is ≥15°C, and the gyro is judged to be failed. Figure 2 and Figure 3 Select the control moment gyro temperature rise data #3 from the four data sets, such as Figure 4 As shown, the feasible domain problem of the control moment gyro quantization process parameters under the allowable life performance prediction deviation is analyzed and studied.

[0132] Since the measurement error parameter μ ε It is usually difficult to identify based on degradation data. In this embodiment, a simple case is considered to estimate the life deviation, that is, μ ε = 0. By using the maximum likelihood estimation to identify the control moment gyro temperature rise data #3, the model parameter estimation results can be obtained. The specific results are shown in Table 1. Table 1 is the model parameter estimation values.

[0133] Table 1

[0134] parameter Estimation results Drift coefficient λ 0.000883 <![CDATA[Diffusion coefficient σ B > 0.03 <![CDATA[Standard deviation of measurement error σ ε > 1.732

[0135] Substitute the above model parameter results into the life expression under the first arrival time, and then obtain the equipment life distribution considering the influence of quantization error. Through the expression of KL distance, the KL distance with the equipment life distribution is calculated as D KL (T ε,e||T)=0.1035.

[0136] like Figure 5 As shown, Figure 5 The lifetime prediction deviation D is shown under different quantization error parameter values. KL (T ε,e ||T). Obviously, only when the quantization error does not exist, that is, when the quantization error parameter q=ba=0, the minimum value of the life estimation deviation will be considered. Since the measurement error always exists, the life prediction deviation D KL (T ε,e ||T)≠0.

[0137] In this embodiment, the quantization error parameter q, that is, the quantization step size q, is q=ba.

[0138] like Figure 6 As shown, Figure 6 The PDF of the estimated life span is given as a function of the quantization step size q. The black line represents the result of the true degradation life span distribution, and the other blue dotted lines represent the PDF of the estimated life span of the device under different quantization step sizes q. It can be found that the height of the PDF continues to move upward with the increase of the quantization step size q.

[0139] In this embodiment, in order to ensure that the prediction result falls within the allowable range, a suitable quantization step size can be selected to reduce the influence of the quantization error. Using the method of step S3, the present invention can effectively determine the feasible area of ​​the quantization error parameter within the maximum allowable range of life prediction while maintaining a constant measurement error. Given D max ={0.05, 0.1, 0.15, 0.2}, the feasible domain of the measurement error and quantization error of the control moment gyro is calculated as follows Figure 7 shown.

[0140] In this embodiment, in summary, since the temperature rise data of the control moment gyro is affected by both measurement error and quantization error, the accuracy of the life estimation is deviated. By calculating the feasible domain of the measurement error and quantization error parameters within the performance allowable range to select a suitable quantization step, the credibility of the estimation result can be improved and the timeliness and effectiveness of maintenance can be ensured.

Claims

1. A feasible domain analysis method for quantitative process parameters of degraded equipment under prediction performance constraints, characterized in that: The following steps are involved: S1. Based on the Wiener process, the equipment degradation process is constructed under the influence of measurement error. The uniform quantizer is used to describe the quantization error caused by the digital-to-analog conversion during the equipment data transmission process, and the equipment life prediction is solved. The estimated results of the equipment estimated life with measurement error and quantization error, and the expectation and variance of the equipment estimated life distribution are obtained respectively; S2. Based on the expectation and variance of the estimated life distribution of the equipment, a performance metric is established to measure the difference between the actual life distribution of the equipment and the estimated life distribution of the equipment; S3. Given the allowable range conditions for life prediction, use the performance measurement criteria to solve the feasible domain of the quantified process parameters of the degraded equipment and complete the feasible domain analysis of the quantified process parameters of the degraded equipment.

2. The feasible domain analysis method for quantizing process parameters of degraded equipment under prediction performance constraints according to claim 1 is characterized in that: The S1 comprises the following steps: S101. Define the equipment life as the time when the degradation process exceeds the failure threshold for the first time, and construct a degradation process with measurement error based on the RUL estimation method of the Wiener process; S102, according to the degradation process containing measurement error, a uniform quantizer is used to describe the quantization error caused by analog-to-digital conversion in the device data transmission project, which is defined as an observed degradation process, and the quantization process parameters include measurement error parameters and quantization error parameters, and the feasible domain of the measurement error parameters and the quantization error parameters is defined; S103, constructing an actual observed degradation process according to the functional relationship between the observed degradation process and the degradation process containing measurement errors and the real degradation process of the equipment; S104. Based on the actual observed degradation process, the PDF form corresponding to the estimated life of the equipment is derived using the total probability formula, and according to the properties of the truncated normal distribution, the PDF form corresponding to the transformed estimated life of the equipment is obtained, and the expectation and variance of the distribution of the estimated life of the equipment are calculated.

3. The feasible domain analysis method for quantizing process parameters of degraded equipment under prediction performance constraints according to claim 2 is characterized in that: The expressions of the feasible domains of the measurement error parameters and the quantization error parameters are as follows: T=inf{t:X(t)≥ω|X(0)<ω} T ε,e =inf{t:Y(t)≥ω|Y(0)<ω} in, represents the feasible domain of measurement error parameters and quantization error parameters of the degradation process, θ ε,e represents the model parameters, D(T ε,e ,T) represents the equipment life T and the estimated equipment life T with measurement error and quantization error ε,e The deviation function between max represents the maximum allowable life prediction deviation, T ε,e represents the estimated lifetime of the device with measurement error and quantization error, T represents the true lifetime of the device, inf{·} represents the infimum of the elements in the set, X(t) represents the true degradation process of the device, X(0) represents the initial degradation state of the device, t represents time, ω represents the failure threshold, Y(t) represents the observed degradation process, Y(0) represents the initial observed degradation state, qu(·) represents a nonlinear mapping function of a uniform quantizer, It represents the degradation process containing measurement error, ε(t) represents the measurement error corresponding to the device at time t, and e(t) represents the quantization error caused by the digital-to-analog conversion at time t.

4. The feasible domain analysis method for quantizing process parameters of degraded equipment under prediction performance constraints according to claim 2 is characterized in that: The expression of the actual observed degradation process is as follows: in, represents a degradation process with measurement error, ε(t) represents the measurement error at time t and obeys Gaussian distribution μ ε and Both represent measurement error parameters, e t represents the quantization error caused by the digital-to-analog conversion at time t, and obeys the uniform distribution e t ~U(a,b), a and b represent the upper and lower bound parameters of the uniform distribution, q represents the quantization error parameter, and q=ba, X(t) represents the actual degradation process of the device, X(0) represents the initial degradation state of the device, Y(t) represents the actual observed degradation process, λ represents the individual characteristics of the degradation of the same batch of devices, B(t) represents the standard Brownian motion, σ B B(t) represents the diffusion term of the degradation process, σ B represents the diffusion coefficient of the degradation process.

5. The feasible domain analysis method for quantizing process parameters of degraded equipment under prediction performance constraints according to claim 2 is characterized in that: The estimated life of the equipment is T ε,e PDF format The expression is as follows: in, represents the initial measurement data with measurement error, y0 represents the initial monitoring data with quantization error, exp(·) represents the natural exponential function, Φ(·) represents the distribution function of the standard normal distribution, t represents time, ω represents the failure threshold, μ ε and Both represent measurement error parameters, and a and b represent the upper and lower bound parameters of the uniform distribution.

6. The feasible domain analysis method for quantizing process parameters of degraded equipment under prediction performance constraints according to claim 5 is characterized in that: The estimated life of the transformed equipment is T ε,e Corresponding PDF format The expression is as follows: Where y0 represents the initial monitoring data with quantization error, exp(·) represents the natural exponential function, Φ(·) represents the distribution function of the standard normal distribution, t represents time, ω represents the failure threshold, μ ε and Both represent measurement error parameters, and a and b represent the upper and lower bound parameters of the uniform distribution.

7. The feasible domain analysis method for quantizing process parameters of degraded equipment under prediction performance constraints according to claim 2 is characterized in that: The S2 comprises the following steps: S201. Based on the estimated results of the estimated life of the equipment, the expectation and variance of the estimated life of the equipment are used to characterize the difference between the actual life of the equipment and the estimated life of the equipment based on the relative increase rate of the coefficient of variation method; wherein the relative increase rate of the coefficient of variation R ξ (T ε,e ,T) is as follows: Among them, ξ(T ε,e ) represents the estimated life of the equipment T ε,e ξ(T) represents the coefficient of variation of the actual life of the equipment T; S202. Based on the estimated result of the estimated life of the equipment, and the expectation and variance of the estimated life distribution of the equipment, define the relative increase rate of variance, and use the relative increase rate of the coefficient of variation and the relative increase rate of variance as performance measurement criteria for measuring the difference between the equipment life distribution and the estimated life distribution of the equipment; wherein the relative increase rate of variance R var (T ε,e ,T) is as follows: Among them, var(T ε,e ) represents the estimated life of the equipment T ε,e The variance of the distribution, var(T) represents the variance of the distribution of the true life of the equipment T.

8. The feasible domain analysis method for quantizing process parameters of degraded equipment under prediction performance constraints according to claim 7 is characterized in that: The S3 comprises the following steps: S301, given the allowable range conditions of life prediction, combined with the relative increase rate of the variation coefficient, determine the feasible domain of the quantized process parameters under the relative increase rate of the variation coefficient; S302. Given the allowable range conditions for life prediction, combined with the relative increase rate of variance, determine the feasible domain of the quantitative process parameters under the relative increase rate of variance, and complete the feasible domain analysis of the quantitative process parameters of the degraded equipment.

9. The feasible domain analysis method for quantizing process parameters of degraded equipment under prediction performance constraints according to claim 8 is characterized in that: The measurement error parameter μ under the relative increase rate of the variation coefficient ε and And the expressions of the feasible domain of the quantization error parameter q are as follows: Among them, R ξ (T ε,e ,T) represents the relative increase rate of the coefficient of variation, ξ(T ε,e ) represents the estimated life of the equipment T ε,e The coefficient of variation of ξ(T) represents the coefficient of variation of the actual life of the equipment T, D max represents the maximum allowable life prediction deviation, λ represents the individual characteristics of the degradation of the same batch of equipment, σ B represents the process parameter, ω represents the failure threshold, and y0 represents the initial monitoring data with quantization error.

10. The feasible domain analysis method for quantizing process parameters of degraded equipment under prediction performance constraints according to claim 8, characterized in that: The measurement error parameter μ under the relative increase rate of variance ε and And the expressions of the feasible domain of the quantization error parameter q are as follows: Among them, λ represents the individual characteristics of the degradation of the same batch of equipment, σ B represents the process parameter, ω represents the failure threshold, y0 represents the initial monitoring data with quantization error, υ min Relative rate of increase of variance R var (T ε,e ,T) lower limit,υ max Relative rate of increase of variance R var (T ε,e ,T)’s upper limit.

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