A Method for Instrument Signal Drift Modeling and Reliability Assessment Based on Multivariate Adaptive Regression Spline Model

Abstract

This invention relates to the field of reliability design analysis, specifically to a method for instrument signal drift modeling and reliability assessment based on a multivariate adaptive regression spline model. The main steps are as follows: (1) establishing an instrument signal drift model based on MARS; (2) characterizing the uncertainty of the MARS model parameters; (3) collecting experimental data and extracting MARS model parameters; (4) estimating the unknown parameters of the MARS model; (5) establishing a reliability model for instrument signal drift; (6) generating a virtual instrument signal drift curve based on Monte Carlo simulation; (7) predicting instrument lifespan; and (8) assessing the instrument lifespan distribution and reliability. The beneficial effects of this invention are: it can accurately quantify and characterize the nonlinear and uncertain characteristics of signal drift, quickly and efficiently assess instrument reliability, and greatly save physical testing time. This method has potential practical application value in the quantitative characterization and reliability assessment of time-varying data with strong nonlinearity and high uncertainty.

Description

Technical Field

[0001] This invention relates to the field of reliability design analysis, specifically to a method for instrument signal drift modeling and reliability assessment based on a multivariate adaptive regression spline model. Background Technology

[0002] The rapid development of information technology has led to the increasing application of artificial intelligence (AI) in instrumentation. Compared to traditional mechanical instruments, intelligent instruments offer significant advantages in self-diagnosis, remote communication, human-computer interaction, and data processing, and are currently widely used in aerospace, nuclear power, petrochemical, metallurgy, and manufacturing industries. However, the application of AI in instrumentation largely relies on the use of complex analog-digital circuits. Therefore, signal drift becomes more pronounced in intelligent instruments. This signal drift introduces errors into the instrument's output signal, resulting in inaccurate results, potentially causing interruptions in industrial processes, and in severe cases, even accidents leading to economic losses and personal injury.

[0003] Smart instruments often operate in harsh, high-temperature environments, where signal drift exhibits highly nonlinear and uncertain characteristics. In existing research, the Multivariate Adaptive Regression Splines (MARS) model, due to its superior ability to handle complex nonlinear problems, can effectively adapt to the nonlinear relationship between input and output and provide accurate predictions, making it suitable for solving the nonlinear modeling problem of smart instrument signal drift. However, a suitable method is currently lacking for quantifying and characterizing the uncertainty features of smart instruments.

[0004] The fundamental cause of signal drift uncertainty in smart instruments lies in the uncertainties of material, process, and environmental parameters on their internal circuit boards. These uncertainties collectively affect the instrument, ultimately causing significant drift in the output signal. However, a smart instrument is a complex and large system composed of multiple circuit boards, each integrating numerous components. This extreme complexity poses a significant challenge to traditional circuit simulation methods. In this context, employing a data-driven approach to establish a signal drift uncertainty characterization model using collected real signal drift data becomes a promising solution.

[0005] Based on the above background, this invention provides a method for instrument signal drift modeling and reliability assessment based on a multivariate adaptive regression spline model. The MARS model is used to model the instrument signal drift, and probabilistic statistical methods are used to characterize the uncertainty of the MARS model parameters. Finally, a series of virtual instrument signal drift curves are generated using Monte Carlo simulation to assess the lifetime distribution and reliability of the instrument signal drift. Summary of the Invention

[0006] To fully consider the highly nonlinear and uncertain characteristics of intelligent instrument signal drift and more accurately assess its reliability, this invention provides a method for instrument signal drift modeling and reliability assessment based on a multivariate adaptive regression spline model. This method, based on certain measured data, can quickly and efficiently assess the reliability of instrument signal drift by quantifying its nonlinear and uncertain characteristics, significantly saving time in physical testing. 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 assessment of signal drift data.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: a method for instrument signal drift modeling and reliability assessment based on a multivariate adaptive regression spline model, comprising the following steps:

[0008] Step 1: Model the instrument signal drift using a Multivariate Adaptive Regression Splines (MARS) model, as shown in the following expression:

[0009]

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

[0011] Step 2: Since signal drift often exhibits a similar growth trend, and its uncertainty characteristics are mainly reflected in the difference in its drift rate, based on the MARS model, the uncertainty of β1 and β2 in the MARS model parameters is characterized by probability and statistics.

[0012] Specifically, due to the monotonically increasing characteristic of signal drift, the MARS model parameters are subject to the following constraints:

[0013]

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

[0015]

[0016] Where (-β1) and β2 are two random variables that follow a log-normal distribution; μ1 and σ1 2 Here are the distribution parameters of the random variable (-β1); μ2 and σ2. 2 Let β2 be the distribution parameter of the random variable.

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

[0018] Specifically, high-temperature aging tests should be conducted on N instruments to accelerate the signal drift rate of the intelligent instruments and save testing time. However, the aging test temperature should not exceed 125℃ as specified in the standard. Simultaneously, the MARS model parameters for the N instruments should be extracted, including t, β0, β1, and β2.

[0019] Step 4: Based on the N sets of MARS model parameters extracted in Step 3, estimate the distribution parameters of the probability representation models 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) follow a normal distribution, the sample mean and sample variance are chosen as μ and σ. 2 Unbiased estimator:

[0021]

[0022] Where N is the number of instruments conducting aging tests; β 1i and β 2i Let be the MARS model parameters for the i-th test instrument.

[0023] Meanwhile, based on the unified parameter extraction features of the MARS model, the MARS model parameter t is estimated using equation (5):

[0024]

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

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

[0027]

[0028] Where R(t) is the instrument's reliability function, representing the reliability at time t; N f Let f(t) be a random variable, representing the lifespan of the instrument under the influence of uncertainty; f(t) is the probability density function of this random variable.

[0029] 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, use the uncertainty characterization model of the MARS model parameter established in Step 2, combined with Equation (1), to generate the signal drift curves of M virtual instruments through Monte Carlo simulation method.

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

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

[0032] Where Ω0 is the sample pool containing only the two MARS model parameters β1 and β2; (β1 i ,β2 i ) represents the sample consisting of the parameters of the i-th MARS model; M is the number of samples.

[0033] Subsequently, using the relationship β0=-β1×t in equation (1), M corresponding β0 samples are calculated, forming 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] Where Ω1 is the sample pool containing all MARS model parameters; (β0) i ,β1 i ,β2 i ) represents the sample composed of the parameters of the i-th MARS model.

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

[0037]

[0038] Wherein, Ω2 is a sample pool consisting of the generated virtual instrument signal drift curves; Let be the signal drift curve of the i-th virtual instrument.

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

[0040] Specifically, the signal drift threshold is defined as P. * And calculate when f i (x)=P * The lifespan N of the M virtual instruments generated in step 6 f i =x i , can be represented as:

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

[0042] Where Ω3 is the set consisting of the lifespans of M virtual instruments; f -1 (x) i N is the inverse function of the signal drift function of the i-th virtual instrument; f i Let be the lifespan of the i-th virtual instrument.

[0043] Step 8: Based on the predicted lifespan values ​​of M instruments obtained in Step 7, plot the frequency-instrument lifespan histogram, and evaluate the lifespan distribution and reliability of the instruments based on the reliability model established in Step 5.

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

[0045]

[0046] in, The probability density function estimate of the instrument's lifetime; M is the number of generated virtual instrument signal drift curves; N fi Let be the lifetime of the i-th virtual instrument; h be the bandwidth; and K(·) be the kernel function, typically a normal kernel function, whose expression is as follows:

[0047]

[0048] Subsequently, the reliability of the instrument was evaluated using the reliability model established in step 5. The evaluation results are as follows:

[0049]

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

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

[0052] 2. This invention provides a method for instrument signal drift modeling and reliability assessment based on a multivariate adaptive regression spline model. This method can quickly and efficiently expand the dataset based on a certain amount of measured data, significantly saving time in physical testing, thereby enabling fault prediction and reliability assessment. This method can be used to expand data under small sample conditions, thus providing data support for a series of tasks relying on large amounts of data. Attached Figure Description

[0053] Figure 1 This is a flowchart of an instrument signal drift modeling and reliability assessment method based on a multivariate adaptive regression spline model proposed in this invention;

[0054] Figure 2 This is a schematic diagram of the high-temperature aging test platform built in the embodiment of the present invention;

[0055] Figure 3 This is the fitting result obtained using the MARS model in the embodiment of this invention;

[0056] Figure 4 This is a portion of the signal drift curves of the virtual instrument generated in the embodiments of this invention;

[0057] Figure 5 These are the probability density function and reliability function of the instrument life in the embodiments of this invention. Detailed Implementation

[0058] The present invention will be 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 applies the instrument signal drift modeling and reliability assessment method based on a multivariate adaptive regression spline model proposed in this invention. This implementation case specifically includes the following:

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

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

[0062]

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

[0064] 2. Quantification of uncertainty in MARS model parameters

[0065] Based on the MARS model, probabilistic and statistical methods are used to characterize the uncertainties of β1 and β2 in the MARS model parameters.

[0066] Specifically, due to the monotonically increasing characteristic of signal drift, the MARS model parameters are subject to the following constraints:

[0067]

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

[0069]

[0070] Where (-β1) and β2 are two random variables that follow a log-normal distribution; μ1 and σ1 2 Here are the distribution parameters of the random variable (-β1); μ2 and σ2. 2 Let β2 be the distribution parameter of the random variable.

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

[0072] Adopting such Figure 2 The aging test platform shown conducted a high-temperature aging test at 90°C on seven intelligent pressure transmitters numbered A1-A7. During the test, the seven intelligent pressure transmitters were continuously aged in a temperature chamber for 500 hours, and their output pressure signals were transmitted to a computer data acquisition system via a HART module. Approximately every 48 hours of high-temperature aging, the pressure signal after the transmitter cooled to room temperature and the corresponding aging time were collected.

[0073] Furthermore, such as Figure 3 As shown in Table 1, the pressure signal drift data of the seven pressure transmitters were fitted using a multivariate adaptive regression spline model, and the MARS model parameters were extracted by substituting them into equation (14).

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

[0075]

[0076] 4. MARS Model Parameter Estimation

[0077] Equation (17) is used to estimate the distribution parameters of the two random variables (-β1) and β2 in equation (16). Since ln(-β1) and ln(β2) follow a normal distribution, the sample mean and sample variance are chosen as μ and σ. 2 The estimation results of the unbiased estimators, (-β1) and β2 distribution parameters are shown in Table 2:

[0078]

[0079] Where N is the number of instruments conducting aging tests; β 1i and β 2i Let be the MARS model parameters for the i-th test instrument.

[0080] Table 2. Estimation results of distribution parameters

[0081]

[0082]

[0083] Meanwhile, based on the unified parameter extraction features of the MARS model, the MARS model parameter t is estimated using equation (18):

[0084]

[0085] 5. Instrument signal drift reliability modeling

[0086] The reliability model of instrument signal drift can be characterized as a time-varying reliability function, as shown in equation (19):

[0087]

[0088] Where R(t) is the instrument's reliability function, representing the reliability at time t; N f Let f(t) be a random variable, representing the lifespan of the instrument under the influence of uncertainty; f(t) is the probability density function of this random variable.

[0089] 6. Generation of virtual instrument signal drift curves based on Monte Carlo simulation

[0090] Based on the estimated values ​​of each distribution parameter obtained in Table 2, the MARS model parameters β1 and β2 in Equation (16) are sampled using the Monte Carlo simulation method to generate a sample pool containing 10,000 samples. Then, using the relationship β0 = -β1 × t in Equation (14), β0 corresponding to these 10,000 samples is calculated, forming a sample pool containing all MATS model parameters, which can be specifically expressed as:

[0091] Ω1={(β0 i ,β1 i ,β2 i )i∈N * ,i≤10000} (20)

[0092] Where Ω1 is the sample pool containing all MARS model parameters; (β0) i ,β1 i ,β2 i ) represents the sample composed of the parameters of the i-th group of MARS models.

[0093] Furthermore, the samples in the Ω1 sample pool are substituted into the MARS model of equation (14) to generate signal drift curves for 10,000 virtual instruments. Some of the generated instrument signal drift curves are shown below. Figure 4 middle.

[0094] 7. Instrument life prediction

[0095] In this case, a signal drift exceeding 2.5% of full scale is considered a malfunction. Considering the full scale of the intelligent pressure transmitter used in the test is 0.2 MPa, the signal drift threshold P can be calculated. * =5kPa.

[0096] Furthermore, calculate when f i (x)=P * The lifetime N of 10,000 virtual instruments generated at any time f i =x i .

[0097] 8. Instrument lifespan distribution and reliability assessment

[0098] Based on the calculated lifetimes of 10,000 virtual instruments, a frequency-instrument lifetime histogram was plotted, and the kernel density function was used to evaluate the probability density function of the instrument lifetime.

[0099]

[0100] in, The probability density function estimate of the instrument's lifespan; M is the number of virtual instrument signal drift curves generated, M = 10000; Nfi Let be the lifetime of the i-th virtual instrument; h be the bandwidth, h = 82.00; K(·) be the kernel function, generally a normal kernel function is chosen, and its expression is as follows:

[0101]

[0102] Subsequently, as Figure 5 As shown, the reliability of the instrument is evaluated using the reliability model of equation (19), and the evaluation results are as follows:

[0103]

[0104] The calculation results show that the instrument signal drift modeling and reliability assessment method based on the multivariate adaptive regression spline model proposed in this invention can accurately quantify the uncertainty characteristics of intelligent instrument signal drift and quickly assess its reliability level.

[0105] The parts of this invention not disclosed in detail are well-known technologies in the field.

[0106] Although the illustrative specific embodiments of the present invention have been described above to enable those skilled in the art to understand the invention, it should be understood that the invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the invention as defined and determined by the appended claims, and all inventions utilizing 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: Model the instrument signal drift using a Multivariate Adaptive Regression Splines (MARS) model, as shown in the following expression: in: (tx) + and (xt) + These are basis function pairs of the MARS model; t, β0, β1 and β2 are the model parameters of the MARS model; Step 2: Characterize the uncertainty of β1 and β2 in the MARS model parameters using probabilistic and statistical methods; Step 3: Conduct aging tests on N instruments, collect time-varying signal drift data of each instrument, and substitute them into formula (1) to extract MARS model parameters; Step 4: Based on the N sets of MARS model parameters extracted in Step 3, estimate the distribution parameters of the probability representation models 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, representing the reliability at time t; N f Let be a random variable, representing the lifespan 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, use the uncertainty characterization model of the MARS model parameter established in Step 2, combined with Equation (1), to generate the signal drift curves of M virtual instruments through Monte Carlo simulation method. Step 7: Define the signal drift threshold and use it to calculate the lifetime of the M virtual instruments generated in Step 6; Step 8: Based on the predicted lifespan values ​​of the M instruments obtained in Step 7, plot the frequency-instrument lifespan histogram, and use the kernel density function to evaluate the probability density function of the instrument lifespan, as shown in Equation (3): in: This is an estimate of the probability density function of the instrument's lifespan; M represents the number of virtual instrument signal drift curves generated; N fi Let be the lifespan of the i-th virtual instrument; h represents bandwidth; K(·) is the kernel function; Subsequently, the reliability of the instrument was evaluated using the reliability model established in step 5. The evaluation results are as follows: 。 2. The method for instrument signal drift modeling and reliability assessment based on a multivariate adaptive regression spline model according to claim 1, characterized in that, Step 2 describes the use of probabilistic and statistical methods to characterize the uncertainties of β1 and β2 in the MARS model parameters, specifically as follows: The uncertainty characteristics of the MARS model parameters are characterized by a log-normal distribution of the form (5): 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 method for instrument signal drift modeling and reliability assessment based on a multivariate adaptive regression spline model according to claim 1, characterized in that, Step 4 involves estimating the distribution parameters of the probability representation models of β1 and β2 from Step 2, as well as the MARS model parameter t, to obtain the estimated values ​​of these parameters. Specifically: Equation (6) is used to estimate the distribution parameters of the two random variables (-β1) and β2 in equation (5), and the sample mean and sample variance are selected as unbiased estimators of μ and σ: in: N represents the number of instruments used in the aging test; β 1i and β 2i Let be the MARS model parameters of the i-th test instrument; Meanwhile, based on the unified parameter extraction features of the MARS model, the MARS model parameter t is estimated using equation (7): 。 4. The method for instrument signal drift modeling and reliability assessment based on a multivariate adaptive regression spline model according to claim 1, characterized in that, Step 6, which involves generating the signal drift curves of M virtual instruments using the Monte Carlo simulation method, specifically includes the following steps: Step 6.1: Based on the estimated values ​​of each distribution parameter obtained in Step 4, the MARS model parameters β1 and β2 in Equation (5) are sampled using the Monte Carlo simulation method to generate a sample pool consisting of M virtual samples, which can be specifically expressed as: in: Ω0 is a sample pool containing only the two MARS model parameters, β1 and β2. (β1 i ,β2 i ) represents the sample composed of the parameters of the i-th group of MARS models; M is the number of samples; Step 6.2: Using the relationship β0=-β1×t in equation (1), calculate M corresponding β0 samples 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 ) represents the sample composed of the parameters of the i-th group of MARS models; Step 6.3: Substitute the samples in the Ω1 sample pool into the MARS model of equation (1) to generate the signal drift curves of M virtual instruments, which can be specifically expressed as: in: Ω2 is a sample pool consisting of the drift curves of the generated virtual instrument signals; Let be the signal drift curve of the i-th virtual instrument.

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