Instrument signal drift modeling and reliability evaluation method based on multivariate adaptive regression spline model

Abstract

The invention relates to the field of reliability design analysis, in particular to an instrument signal drift modeling and reliability evaluation method based on a multivariate adaptive regression spline model. The method mainly comprises the following steps: (1) establishing a signal drift model of an instrument based on MARS; (2) the uncertainty of the MARS model parameters is represented; (3) collecting test data and extracting MARS model parameters; (4) estimating unknown parameters of the MARS model; (5) establishing a reliability model of instrument signal drift; (6) generating a virtual instrument signal drift curve based on Monte Carlo simulation; (7) predicting the service life of the instrument; and (8) evaluating the service life distribution and reliability of the instrument. The method has the beneficial effects that the nonlinear and uncertainty characteristics of signal drift can be accurately and quantitatively represented, the reliability of the instrument can be quickly and efficiently evaluated, and the physical test time is greatly saved. The method has potential practical application value in the aspects of quantitative characterization and reliability evaluation of time-varying data with strong nonlinearity and high uncertainty.

Description

Technical Field

[0001] The present invention relates to the field of reliability design analysis, and in particular to an instrument signal drift modeling and reliability evaluation method based on a multivariate adaptive regression spline model. Background Art

[0002] The rapid development of information technology has led to an increasing number of applications of artificial intelligence in instrumentation. Compared with traditional mechanical instruments, intelligent instruments have greater advantages in self-diagnosis, remote communication, human-computer interaction and data processing. They have been widely used in aerospace, nuclear power, petrochemical, metallurgy, manufacturing and other fields. However, the application of artificial intelligence in instrumentation depends largely on the use of complex digital-analog circuits. Therefore, for intelligent instruments, the signal drift phenomenon will become more obvious. Due to the generation of signal drift, the output signal of the instrument will have errors, giving inaccurate results, and ultimately leading to interruptions in the industrial process. In severe cases, it may even cause accidents, resulting in economic losses and casualties.

[0003] Smart instruments often work in harsh high-temperature environments, in which the signal drift of smart instruments has highly nonlinear and uncertain characteristics. In existing research, the Multivariate Adaptive Regression Splines (MARS) model can effectively adapt to the nonlinear relationship between input and output and give accurate prediction results due to its superiority in dealing with complex nonlinear problems. It can be used to solve the nonlinear modeling problem of smart instrument signal drift. However, there is currently no suitable method to quantify the uncertainty characteristics of smart instruments.

[0004] The fundamental reason for the uncertainty of the signal drift of smart instruments is the uncertainty of the material parameters, process parameters and environmental parameters on the internal circuit board. These uncertainties act on the instrument in combination, and ultimately cause the drift of the instrument output signal to produce significant uncertainty characteristics. However, the smart instrument is a complex and large system composed of multiple circuit boards, and each circuit board integrates a large number of components. This extremely high complexity poses a major challenge to traditional circuit simulation methods. In this case, using a data-driven approach to use the collected real signal drift data to establish a signal drift uncertainty characterization model has become a good solution.

[0005] Based on the above background, the present invention provides an instrument signal drift modeling and reliability assessment method based on a multivariate adaptive regression spline model. The signal drift of the instrument is modeled using the MARS model, and the uncertainty of the MARS model parameters is characterized using a probability statistics method. Finally, a series of signal drift curves of virtual instruments are generated using the Monte Carlo simulation method to evaluate the life distribution and reliability of the instrument signal drift. Summary of the invention

[0006] In order to fully consider the highly nonlinear and uncertain characteristics of the intelligent instrument signal drift and more accurately evaluate the reliability level of the intelligent instrument signal drift, the present invention provides an instrument signal drift modeling and reliability evaluation method based on a multivariate adaptive regression spline model. Based on certain measured data, this method can quickly and efficiently evaluate the reliability of the instrument signal drift by quantifying the nonlinear and uncertain characteristics of the signal drift, greatly saving the time of physical experiments. The results of this method can be used to process time-varying data with strong nonlinearity and high uncertainty, and have potential practical application value in the quantitative characterization and reliability evaluation of signal drift data.

[0007] In order to achieve the above object, the present invention adopts the following technical solution: an instrument signal drift modeling and reliability evaluation method based on a multivariate adaptive regression spline model, comprising the following steps:

[0008] Step 1: Use the Multivariate Adaptive Regression Splines (MARS) model to model the instrument signal drift. The expression is as follows:

[0009]

[0010] Among them, (tx) + and (xt) + is the basis function pair of the MARS model; t, β0, β1 and β2 are the model parameters of the MARS model; β0 = -β1×t can be obtained from the characteristics of the zero-crossing point of the signal drift curve.

[0011] Step 2: Since signal drift often shows a similar growth trend, and its uncertainty characteristics are mainly concentrated in the difference in its drift rate, based on the MARS model, the probability statistics method is used to characterize the uncertainty of β1 and β2 in the MARS model parameters.

[0012] Specifically, due to the monotonically increasing characteristics of signal drift, the MARS model parameters have the following constraints:

[0013]

[0014] Therefore, the log-normal distribution in the form of formula (3) is used to characterize the uncertainty characteristics of the MARS model parameters:

[0015]

[0016] Among them, (-β1) and β2 are two random variables that obey the lognormal distribution; μ1 and σ1 2 are the distribution parameters of the random variable (-β1); μ2 and σ2 2 is the distribution parameter of the random variable β2.

[0017] Step 3: Carry out aging tests on N instruments, collect the time-varying data of signal drift of each instrument, and substitute it into equation (1) to extract the MARS model parameters.

[0018] Specifically, a high-temperature aging test of N instruments should be carried out to accelerate the rate of intelligent instrument signal drift and save test time, but the aging test temperature should not exceed 125°C specified in the specification. At the same time, the MARS model parameters of N instruments are extracted, including: t, β0, β1 and β2.

[0019] Step 4: Based on the N groups of MARS model parameters extracted in step 3, estimate the distribution parameters of the probability characterization model of β1 and β2 in step 2 and the MARS model parameter t to obtain the estimated values ​​of the above parameters.

[0020] Specifically, equation (4) is used to estimate the distribution parameters of the two random variables (-β1) and β2 in equation (3). Since ln(-β1) and ln(β2) obey normal distribution, the sample mean and sample variance are selected as μ and σ. 2 An unbiased estimator of :

[0021]

[0022] Where N is the number of instruments used in the aging test; β 1i and β 2i is the MARS model parameter of the i-th test instrument.

[0023] At the same time, based on the unified parameter extraction feature of the MARS model, the MARS model parameter t is estimated using formula (5):

[0024]

[0025] Step 5: Establish a reliability model for instrument signal drift.

[0026] Specifically, the reliability model of instrument signal drift can be expressed in the form of a time-varying reliability function, as shown in formula (6):

[0027]

[0028] Among them, R(t) is the reliability function of the instrument, which represents the reliability at time t; N f is a random variable, which represents the life of the instrument under the influence of uncertainty; f(t) is the probability density function of the random variable.

[0029] Step 6: Based on the distribution parameters of the β1 and β2 probability characterization models obtained in step 4 and the estimated value of the MARS model parameter t, the uncertainty characterization model of the MARS model parameters established in step 2 is used in combination with equation (1) to generate the signal drift curves of the M virtual instruments through the Monte Carlo simulation method.

[0030] Specifically, based on the estimated values ​​of the distribution parameters obtained in step 4, the MARS model parameters β1 and β2 in formula (3) are sampled by the Monte Carlo simulation method to generate a sample pool consisting of M groups of virtual samples, which can be specifically expressed as:

[0031] Ω0={(β1 i ,β2 i )i∈N * ,i≤M} (7)

[0032] Among them, Ω0 is a sample pool containing only two MARS model parameters β1 and β2; (β1 i ,β2 i ) is the sample composed of the i-th group of MARS model parameters; M is the number of samples.

[0033] Then, using the relationship β0=-β1×t in formula (1), M corresponding β0 samples are calculated to form a sample pool containing all MARS model parameters, which can be specifically expressed as:

[0034] Ω1={(β0 i ,β1 i ,β2 i )i∈N * ,i≤M} (8)

[0035] Among them, Ω1 is the sample pool containing all MARS model parameters; (β0 i ,β1 i ,β2 i ) is the sample composed of the i-th group of MARS model parameters.

[0036] Finally, the samples in the Ω1 sample pool are substituted into the MARS model of formula (1) to generate the signal drift curve of M virtual instruments, which can be specifically expressed as:

[0037]

[0038] Among them, Ω2 is the sample pool composed of the generated virtual instrument signal drift curve; is the signal drift curve of the i-th virtual instrument.

[0039] Step 7: Define the signal drift threshold and use it to calculate the lifespan of the M virtual meters generated in step 6.

[0040] Specifically, the signal drift threshold is defined as P * , and calculate when f i (x) = P * The life span N of the M virtual instruments generated in step 6 is f i =x i , which can be expressed as:

[0041] Ω3={N f i =f -1 (x) i |i∈N * ,i≤i≤M} (10)

[0042] Among them, Ω3 is the set of life spans of M virtual instruments; f -1 (x) i is the inverse function of the signal drift function of the i-th virtual instrument; N f i is the life of the i-th virtual instrument.

[0043] Step 8: Based on the life prediction values ​​of the M instruments obtained in step 7, draw a frequency-instrument life histogram, and evaluate the life distribution and reliability of the instruments based on the reliability model established in step 5.

[0044] Specifically, as shown in formula (11), the kernel density function is used to evaluate the probability density function of the instrument life:

[0045]

[0046] in, is the estimated value of the probability density function of the instrument life; M is the number of virtual instrument signal drift curves generated; N fi is the life of the i-th virtual instrument; h is the bandwidth; K(·) is the kernel function, and the normal kernel function is generally used, and its expression is as follows:

[0047]

[0048] Then, the reliability model established in step 5 is used to evaluate the reliability of the instrument. The evaluation results are as follows:

[0049]

[0050] The present invention has the following beneficial effects:

[0051] 1. The present invention provides an instrument signal drift modeling and reliability assessment method based on a multivariate adaptive regression spline model, which can accurately quantify the highly nonlinear and uncertain characteristics of signal drift, thereby carrying out corresponding reliability analysis and assessment work. This method has potential practical application value in processing two-dimensional data with strong nonlinearity and high uncertainty.

[0052] 2. The present invention provides an instrument signal drift modeling and reliability assessment method based on a multivariate adaptive regression spline model, which can quickly and efficiently expand the data set based on certain measured data, greatly saving the time of physical testing, thereby performing fault prediction and reliability assessment. This method can be used to achieve data expansion under small sample conditions, thereby providing data support for a series of work that relies on large batches of data. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 It is a flow chart of an instrument signal drift modeling and reliability evaluation method based on a multivariate adaptive regression spline model proposed by the present invention;

[0054] Figure 2 It is a schematic diagram of a high temperature aging test platform constructed in an implementation case of the present invention;

[0055] Figure 3 is the fitting result obtained by using the MARS model in the implementation case of the present invention;

[0056] Figure 4 It is a signal drift curve of a part of virtual instruments generated in the implementation case of the present invention;

[0057] Figure 5 It is the probability density function and reliability function of the instrument life in the implementation case of the present invention. DETAILED DESCRIPTION

[0058] The present invention is further described below with reference to the accompanying drawings and specific implementation examples.

[0059] This implementation case takes a certain type of intelligent pressure transmitter as the analysis object and studies the signal drift phenomenon of its output pressure signal. Figure 1 The method flow shown in the figure applies a method for modeling and reliability assessment of instrument signal drift based on a multivariate adaptive regression spline model proposed by the present invention. This implementation case specifically includes the following contents:

[0060] 1. Instrument signal drift modeling based on MARS model

[0061] The MARS model is used to model the instrument signal drift, and the expression is as follows:

[0062]

[0063] Among them, (tx) + and (xt) + is the basis function pair of the MARS model; t, β0, β1 and β2 are the model parameters of the MARS model; β0 = -β1×t can be obtained from the characteristics of the zero-crossing point of the signal drift curve.

[0064] 2. Quantification of MARS model parameter uncertainty

[0065] Based on the MARS model, probability statistics method is used to characterize the uncertainty of β1 and β2 in the MARS model parameters.

[0066] Specifically, due to the monotonically increasing characteristics of signal drift, the MARS model parameters have the following constraints:

[0067]

[0068] Therefore, the log-normal distribution in the form of formula (16) is used to characterize the uncertainty characteristics of the MARS model parameters:

[0069]

[0070] Among them, (-β1) and β2 are two random variables that obey the lognormal distribution; μ1 and σ1 2 are the distribution parameters of the random variable (-β1); μ2 and σ2 2 is the distribution parameter of the random variable β2.

[0071] 3. Aging test and MARS model parameter extraction

[0072] Use Figure 2 The aging test platform shown in the figure carries out a high temperature aging test at 90°C for seven intelligent pressure transmitters numbered A1-A7. During the test, the seven intelligent pressure transmitters are aged in the temperature chamber for 500 hours, and the output pressure signals are transmitted to the computer data acquisition system through the HART module. After about 48 hours of high temperature aging, the pressure signal and the corresponding aging time of the transmitter after cooling to room temperature are collected.

[0073] Further, such as Figure 3 As shown in Table 1, the multivariate adaptive regression spline model is used to fit the pressure signal drift data of the seven pressure transmitters collected, and the MARS model parameters are extracted by substituting them into formula (14), as shown in Table 1.

[0074] Table 1 MARS model parameters extracted from seven intelligent pressure transmitters

[0075] 4. MARS model parameter estimation

[0076] Formula (17) is used to estimate the distribution parameters of the two random variables (-β1) and β2 in formula (16). Since ln(-β1) and ln(β2) obey normal distribution, the sample mean and sample variance are selected as μ and σ. 2 The unbiased estimator of , the estimation results of (-β1) and β2 distribution parameters are shown in Table 2:

[0077]

[0078] Where N is the number of instruments used in the aging test; β 1i and β 2i is the MARS model parameter of the i-th test instrument.

[0079] Table 2 Distribution parameter estimation results

[0080] At the same time, based on the unified parameter extraction feature of the MARS model, the MARS model parameter t is estimated using formula (18):

[0081]

[0082] 5. Instrument signal drift reliability modeling

[0083] The reliability model of instrument signal drift can be expressed in the form of a time-varying reliability function, as shown in formula (19):

[0084]

[0085] Among them, R(t) is the reliability function of the instrument, which represents the reliability at time t; N f is a random variable, which represents the life of the instrument under the influence of uncertainty; f(t) is the probability density function of the random variable.

[0086] 6. Generation of virtual instrument signal drift curve based on Monte Carlo simulation

[0087] Based on the estimated values ​​of the distribution parameters obtained in Table 2, the MARS model parameters β1 and β2 in equation (16) are sampled by Monte Carlo simulation method to generate a sample pool containing 10,000 groups of samples. And using the relationship β0 = -β1×t in equation (14), the β0 corresponding to these 10,000 samples is calculated to form a sample pool containing all MATS model parameters, which can be specifically expressed as:

[0088] Ω1={(β0 i ,β1 i ,β2 i )i∈N * ,i≤10000} (20)

[0089] Among them, Ω1 is the sample pool containing all MARS model parameters; (β0 i ,β1 i ,β2 i ) is the sample composed of the i-th group of MARS model parameters.

[0090] Furthermore, the samples in the Ω1 sample pool are substituted into the MARS model of formula (14) to generate the signal drift curves of 10,000 virtual instruments. Some of the generated instrument signal drift curves are shown in Figure 4 middle.

[0091] 7. Instrument life prediction

[0092] In this case, it is stipulated that a signal drift exceeding 2.5% of the full scale is considered to be a fault. Considering that the full scale of the intelligent pressure transmitter used in the test is 0.2MPa, the signal drift threshold P can be calculated. * =5kPa.

[0093] Furthermore, when f i (x) = P * The lifetime N of 10,000 virtual instruments generated at f i =x i .

[0094] 8. Instrument life distribution and reliability assessment

[0095] Based on the calculated lifespan of 10,000 virtual instruments, a frequency-instrument life histogram is drawn, and the kernel density function is used to evaluate the probability density function of the instrument life:

[0096]

[0097] in, is the estimated value of the probability density function of the instrument life; M is the number of virtual instrument signal drift curves generated, M = 10000; Nfi is the life of the i-th virtual instrument; h is the bandwidth, h = 82.00; K(·) is the kernel function, and the normal kernel function is generally used, and its expression is as follows:

[0098]

[0099] Then, if Figure 5 As shown, the reliability model of formula (19) is used to evaluate the reliability of the instrument, and the evaluation results are as follows:

[0100]

[0101] It can be seen from the calculation results that the instrument signal drift modeling and reliability assessment method based on the multivariate adaptive regression spline model proposed in the present invention can accurately quantify the uncertainty characteristics of the intelligent instrument signal drift and quickly assess its reliability level.

[0102] Parts of the present invention that are not disclosed in detail belong to the common knowledge in the art.

[0103] Although the above describes the illustrative specific embodiments of the present invention to facilitate those skilled in the art to understand the present invention, it should be clear that the present invention is not limited to the scope of the specific embodiments. 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 using the concept of the present invention are protected.

Claims

1. A method for instrument signal drift modeling and reliability assessment based on a multivariate adaptive regression spline model, characterized in that: The implementation steps include the following: Step 1: Use the Multivariate Adaptive Regression Splines (MARS) model to model the instrument signal drift. The expression is as follows: in: (tx) + and (xt) + is the basis function pair of the MARS model; t, β0, β1 and β2 are the model parameters of the MARS model; Step 2: Use probability statistics methods to characterize the uncertainty of β1 and β2 in the MARS model parameters; Step 3: Carry out aging tests on N instruments, collect the time-varying data of signal drift of each instrument, and substitute it into formula (1) to extract the MARS model parameters; Step 4: Based on the N groups of MARS model parameters extracted in step 3, estimate the distribution parameters of the probability representation model of β1 and β2 in step 2 and the MARS model parameter t to obtain the estimated values ​​of the above parameters; Step 5: Establish a reliability model for instrument signal drift as shown below; in: R(t) is the reliability function of the instrument, indicating the reliability at time t; N f is a random variable, which represents the life of the instrument under the influence of uncertainty; f(t) is the probability density function of the random variable; Step 6: Based on the distribution parameters of the probability characterization model of β1 and β2 obtained in step 4 and the estimated value of the MARS model parameter t, the uncertainty characterization model of the MARS model parameters established in step 2 is used, combined with formula (1), and the signal drift curves of M virtual instruments are generated by Monte Carlo simulation method; Step 7: Define the signal drift threshold and use it to calculate the life of the M virtual instruments generated in step 6; Step 8: Based on the predicted life values ​​of the M instruments obtained in step 7, draw a frequency-instrument life histogram, and use the kernel density function to evaluate the probability density function of the instrument life, as shown in formula (3): in: is the estimated value of the probability density function of the instrument life; M is the number of virtual instrument signal drift curves generated; N fi is the life of the i-th virtual instrument; h is the bandwidth; K(·) is the kernel function; Then, the reliability model established in step 5 is used to evaluate the reliability of the instrument. The evaluation results are as follows:

2. The instrument signal drift modeling and reliability assessment method based on a multivariate adaptive regression spline model according to claim 1 is characterized in that: The probability statistics method described in step 2 is used to characterize the uncertainty of β1 and β2 in the MARS model parameters, specifically: The log-normal distribution of the form (5) is used to characterize the uncertainty characteristics of the MARS model parameters: in: (-β1) and β2 are two random variables that follow a log-normal distribution; μ1 and σ1 are the distribution parameters of the random variable (-β1), and μ2 and σ2 are the distribution parameters of the random variable β2.

3. The instrument signal drift modeling and reliability assessment method based on a multivariate adaptive regression spline model according to claim 1 is characterized in that: Step 4 estimates the distribution parameters of the probability characterization model of β1 and β2 in step 2 and the MARS model parameter t to obtain the estimated values ​​of the above parameters, specifically: Formula (6) is used to estimate the distribution parameters of the two random variables (-β1) and β2 in formula (5), and the sample mean and sample variance are selected as unbiased estimators of μ and σ: in: N is the number of instruments for aging test; β 1i and β 2i is the MARS model parameter of the i-th test instrument; At the same time, based on the unified parameter extraction feature of the MARS model, the MARS model parameter t is estimated using formula (7):

4. The instrument signal drift modeling and reliability assessment method based on a multivariate adaptive regression spline model according to claim 1 is characterized in that: The method of generating the signal drift curves of M virtual instruments by Monte Carlo simulation method in step 6 specifically includes the following steps: Step 6.1: Based on the estimated values ​​of the distribution parameters obtained in step 4, the MARS model parameters β1 and β2 in equation (5) are sampled by the Monte Carlo simulation method to generate a sample pool consisting of M groups of virtual samples, which can be specifically expressed as: in: Ω0 is a sample pool containing only two MARS model parameters β1 and β2; (β1 i ,β2 i ) is the sample composed of the i-th group of MARS model parameters; M is the number of samples; Step 6.2: Using the relationship β0=-β1×t in formula (1), M corresponding β0 samples are calculated to form a sample pool containing all MARS model parameters, which can be specifically expressed as: in: Ω1 is the sample pool containing all MARS model parameters; (β0 i ,β1 i ,β2 i ) is the sample composed of the i-th group of MARS model parameters; Step 6.3: Substitute the samples in the Ω1 sample pool into the MARS model of formula (1) to generate the signal drift curves of M virtual instruments, which can be specifically expressed as: in: Ω2 is the sample pool composed of the generated virtual instrument signal drift curve; is the signal drift curve of the i-th virtual instrument.

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