CN115048868B - Evaluation method of uncertainty of dynamic measurement system based on time sequence neural network - Google Patents
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Abstract
The invention discloses a method for evaluating uncertainty of a dynamic measurement system based on a neural network method, which comprises the following steps: establishing a data set, modeling the neural network, modeling the data set by using a neural network architecture, realizing propagation rule identification of measurement uncertainty by using a method of integrating the neural network, improving performance and realizability of the model by using a loss function obtained by modeling by using a Bayesian method, and predicting output and uncertainty of the model based on the integrated neural network. According to the invention, the modeling of the dynamic measurement system by the neural network capable of processing the time sequence signals is adopted, compared with the traditional method for measuring the uncertainty by the dynamic measurement system, the uncertainty of the model and the uncertainty of data can be independently assessed, the model prediction is more accurate, and the uncertainty assessment result is more in accordance with engineering application practice.
Description
Technical Field
The invention belongs to the technical field of reliability analysis, and particularly relates to a method for evaluating uncertainty of a dynamic measurement system based on a neural network.
Background
GUM Guide to the Expression of Uncertainty in Measurement establishes an uncertainty representation system, and a complete measurement framework is provided for evaluating the uncertainty of static measurement. However, in the case of a dynamic measurement system, since the system state changes with time, the measured state also changes with time, and the condition of using the GUM as a way of evaluating uncertainty is no longer satisfied. The proposed complementary versions GUM-S1 and GUM-S2 solve the problem of uncertainty representation guideline in the aspect of dynamic measurement uncertainty quantification, and the discussion of whether a model is linear or nonlinear is avoided through the introduction of probability density functions.
On this basis, researchers have proposed some representation methods of dynamic uncertainties, such as bayesian methods, filter methods, and the like. The Bayesian method can obtain posterior distribution according to prior distribution, and can be combined with various factors, including current dynamic measurement data, expert opinion and the like to predict data at a certain moment in the future. But the difficulty is that a priori distributions are difficult to obtain and posterior distributions are often difficult to calculate, often approximating posterior distributions with likelihood functions. Researchers have proposed various approaches to bayesian distributions, such as dropout, variational distribution, etc., which are mostly computationally intensive. Whereas the linear filter approach has difficulty in dealing with the nonlinear system problems most common in dynamic measurement systems.
In recent years, neural networks exhibit powerful mapping capabilities in modeling computation that can be used to model approaches to any linear and nonlinear system, but their degree of trustworthiness remains to be appreciated. The existing neural network uncertainty evaluation modes mainly comprise a network integration method, a Bayesian method, a test time data enhancement method, a single deterministic method and the like. The invention applies the strong modeling capability and the capability of quantifying uncertainty of the neural network to the dynamic measurement system, and supplements the blank of modeling by using the neural network for uncertainty of the dynamic measurement system.
Disclosure of Invention
The invention aims to supplement the gap of modeling and quantifying the uncertainty of a dynamic measurement system by using a time sequence neural network method.
The invention solves the technical problems by the following method:
The method for evaluating the uncertainty of the dynamic measurement system based on the time sequence neural network comprises the following steps:
step S1, sample data acquisition, namely taking input data and output data of a dynamic measurement system as training data based on known model parameters and modeling processes of the dynamic measurement system;
Step S2, data processing is carried out, training data are preprocessed, each group of input data and corresponding output data are adjusted to be the same dimension and size, and time dimension slice reconstruction is carried out on long-sequence input signals;
step S3, modeling a neural network;
Two independent feedforward neural network structures are built in a single network, wherein one feedforward neural network structure is a neural network capable of processing time sequence information and is used for outputting an estimated value mean value x n; the other feedforward neural network is a linear feedforward neural network, and is used for outputting an estimated value variance sigma 2;
S4, loss function calculation and network training;
Calculating loss of the output x n and the true value x t of the neural network by adopting an MSE loss function, reversely transferring errors, carrying out optimization approximation by using a random gradient descent method, and training a single network by maximizing posterior distribution of an estimated mean value;
step S5: neural network integration;
And inputting the test data into a trained integrated network, and respectively quantifying the data uncertainty and the model uncertainty.
The preferred technical scheme provided by the invention is as follows:
The step S1 specifically includes collecting M groups of dynamic time-related signals X 1、X2、X3...XM in batch, where each group of dynamic time-related signals have the same frequency, different peak values, and different time of occurrence of the peak values, and the input signal X t (t=1, 2,..n) serving as a dynamic measurement system is a function of time t, and the time sequence length is N;
under the input signal, the dynamic measurement system generates M sets of corresponding system output signals Y 1、Y2、Y3...YM, each set of output signals Y t (t=1, 2,.,. N); the output y t at each time t follows a normal distribution, with a probability density function of η t (t=1, 2, n.), the joint probability density function of the entire time sequence is encoded as The probability density function of the dynamic measurement system output sequence is:
matching each set of input and output signals as a sample dataset, wherein the K (K < M) sets are used as training data, the remainder being used as test data;
the invention provides another preferable technical scheme that: wherein,
In step S3, the inverse measurement process of the dynamic measurement system of step S1 is modeled using the neural network capable of processing the timing information, and the output signal y t of the dynamic measurement system is used as the input signal y n of the neural network (n=1, 2, n.), the neural network output x n (n=1, 2,.., N) is used as the input estimate value for the back-measurement dynamic measurement system, and the input signal x t of the step S1 dynamic measurement system is used as the output true value for the neural network.
The further preferable technical scheme provided by the invention is as follows: wherein,
The step S4 specifically comprises the following steps:
Since the output y t of the dynamic measurement system at each time t is subject to a normal distribution, the probability density function is η t (t=0, 1,2,..once., N), and the joint probability density function of the whole time sequence is encoded as The probability density function of the dynamic measurement system output
A data prior distribution P (y n) as a neural network;
(1) Calculating loss1 of x n and x t using the MSE function;
(2) According to the Bayesian theorem, the input and the output follow normal distribution, the input Y n and the theta are variables, the probability density function P (Y|X) in the step S1 is used as the known data prior distribution of the neural network input Y n, and a scheme of adding Gaussian noise to Y n is adopted to replace P (Y|X);
The neural network is modeled as:
P(xt|yn,θ)＝N(xt;xn,σ2) (2)
The objective is to obtain the estimated mean x n and variance σ 2 of the true value x t. Likelihood function to maximize posterior prediction distribution:
Where N is the time series length, taking the negative value of the natural logarithm of the likelihood function as loss2:
the final total loss is:
loss＝loss1+loss2 (5)
Training is stopped when the sample is trained 1000 times or the gradient of the objective function is no longer reduced.
The most preferable technical scheme provided by the invention is as follows: wherein,
The step S5 specifically comprises the following steps:
Inputting test data, storing the output of each network in step S5 and calculating the sample mean value And variance s 2:
model uncertainty is the overall variance:
The uncertainty of the model of the integrated method is represented by a confidence interval method according to GUM, the uncertainty of the model is mainly caused by the architecture of the model, the training process and the region with insufficient representativeness in training data, the confidence level is taken to be 95%, and the estimated value is taken Expressed as:
The uncertainty u 1D of the data output by the single network consists of two uncertainty components of the uncertainty u x of the input signal Yn and the uncertainty u θ of the network parameter theta, and the uncertainty propagation is realized by solving a Bayesian conditional probability formula (2);
The uncertainty u 1D of the neural network output Xn contains the uncertainty of the input signal Yn and the network parameter θ;
the uncertainty of the data of the integrated network is obtained by averaging the standard deviation sigma=u 1D of the output of each network conforming to the normal distribution:
The uncertainty of the data is mainly caused by data noise, the confidence level is taken to be 95%, and the estimated value is taken Expressed as:
finally, summing the model uncertainty and the data uncertainty as a total uncertainty:
ut＝um+uD (11)
the beneficial effects of the invention include:
1. the neural network method capable of processing the time sequence information is adopted to model the dynamic measurement system, so that the method not only can approximate to a linear system, but also can make good mapping on a nonlinear relation, and has strong generalization capability.
2. The input and output of the dynamic measurement system have strong time sequence dependence, the current output depends on the current input and is influenced by the past input, and the one-to-one mapping relation of the traditional neural network is not suitable for modeling of the dynamic measurement system. The neural network capable of processing the time sequence information can well memorize the past information and act on the current output, and has good similarity with the mechanism of the dynamic measurement system.
3. The uncertainty of the estimated value is quantified by using a neural network integration method, and the situation that the final uncertainty change trend is the same as the model input due to the dependence of uncertainty propagation on the model input in the traditional method is avoided. And the model uncertainty and the data uncertainty are independently assessed.
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In order to more clearly illustrate the embodiments of the invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, it being obvious that the drawings in the following description are only some embodiments of the invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a simplified flow chart of the method of the present invention;
FIG. 2 is an example of input and output signals of a dynamic measurement system according to the present invention;
FIG. 3 is a graph of input and output signals of the dynamic measurement system of the present invention integrated with neural network modeling;
FIG. 4 shows the model uncertainty (a) and the data uncertainty (b) after network integration according to the present invention;
fig. 5 is a diagram of the total uncertainty after network integration of the present invention.
Detailed Description
The technical solutions of the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings.
As shown in the flow chart of fig. 1, the method for evaluating uncertainty of a dynamic measurement system based on a time sequence neural network comprises the following steps:
step S1, sample data acquisition, namely taking input data and output data of a dynamic measurement system as training data based on known model parameters and modeling processes of the dynamic measurement system;
In order to model a dynamic measurement system using a time-series neural network, input and output data of the dynamic measurement system are required as training data. The invention refers to a method of a filter to establish a second-order linear time-invariant dynamic measurement system. As shown in fig. 2, the dynamic measurement system inputs are gaussian-like impulse signals and outputs as continuously decaying system response signals. Since the system inputs are agnostic, the goal of neural network modeling is to approximate the inverse measurement process of a dynamic measurement system from building a mapping of system outputs to system inputs, and to quantify the uncertainty of the input estimates.
100 Groups of response signals Y 1、Y2、Y3...Y100 corresponding to 100 groups of output by a second-order dynamic measurement system established by using an IIR filter are collected, wherein the peak values of the 100 groups are different, the impulse time is different, and the frequencies of the Gaussian-like impulse signals X 1、X2、X3...X100 are the same. Of which 90 groups are used as training data and the remaining 10 groups are used as test data.
Step S2, data processing is carried out, training data are preprocessed, each group of input data and corresponding output data are adjusted to be the same dimension and size, and time dimension slice reconstruction is carried out on long-sequence input signals;
the raw data is an ultra-long time series signal x t (t=1, 2,..2000), the dimension of the input is changed by means of slice reconstruction in the time dimension. The neural network inputs the signal values of 8 time points each time until the signal is finished, so that huge calculation amount caused by single time point-by-point processing is avoided, and the operation speed is improved.
Step S3, modeling a neural network;
Two independent feedforward neural network structures are built in a single network, wherein one feedforward neural network structure is a neural network capable of processing time sequence information and is used for outputting an estimated value mean value x n; the other feedforward neural network is a linear feedforward neural network, and is used for outputting an estimated value variance sigma 2;
The single neural network comprises two independent network structures, and the mean and the variance of the measured estimated values are respectively output. For the average value, since the input and output are time series data, there is a strong time sequence dependence, and the current output is determined by the past input and the current input, instead of a simple one-to-one mapping relationship. The present example employs a special network structure LSTM of RNN. LSTM is a long and short term memory network that can be used to process long time series of data due to its special structure. For variance, a general linear feed forward neural network is employed.
S4, loss function calculation and network training;
Calculating loss of the output x n and the true value x t of the neural network by adopting an MSE loss function, reversely transferring errors, and carrying out optimization approximation by using a random gradient descent method;
Since the output y t of the dynamic measurement system at each time t is subject to a normal distribution, the probability density function is η t (t=0, 1,2,..once., N), and the joint probability density function of the whole time sequence is encoded as The probability density function of the dynamic measurement system output
The data a priori distribution P (y n) as a neural network.
(1) Wherein the LSTM network outputs an estimated value mean value x n, and in order to make x n approach to a true value x t, the loss1 of x n and x t is calculated by using an MSE function;
(2) According to the Bayesian theorem, the input and the output follow normal distribution, the input Y n and the theta are variables, the probability density function P (Y|X) in the first step is taken as the known data prior distribution of the neural network input Y n, and a scheme of adding Gaussian noise to Y n is adopted to replace P (Y|X). The neural network is modeled as:
P(xt|yn,θ)＝N(xt;xn,σ2) (2)
The objective is to obtain the estimated mean x n and variance σ 2 of the true value x t. Likelihood function to maximize posterior prediction distribution:
Where N is the time series length, taking the negative value of the natural logarithm of the likelihood function as loss2:
the final total loss is:
loss＝loss1+loss2 (5)
Training is stopped when the sample is trained 1000 times or the gradient of the objective function is no longer reduced.
The training results of the single neural network are shown in fig. 3, and have good fitting results for input signals different from those of training.
100 Neural networks of the same structure were trained, with each neural network training iteration number of 1000. The network parameters are reserved and numbered after each training, and the training results are different each time due to the randomness of the learning of the network.
Step S5: and inputting the test data into a trained integrated network, and respectively quantifying the data uncertainty and the model uncertainty.
Inputting test data, storing the output of each network and calculating the sample mean valueAnd variance s 2:
model uncertainty is the overall variance, as shown in fig. 4 (b):
The uncertainty of the model of the integrated method is represented by a confidence interval method according to GUM, the uncertainty of the model is mainly caused by the architecture of the model, the training process and the region with insufficient representativeness in training data, the confidence level is taken to be 95%, and the estimated value is taken Expressed as:
The data uncertainty u 1D of the single network output consists of two uncertainty components of the uncertainty u x of the input Yn and the uncertainty u θ of the network parameter θ, and the uncertainty propagation is realized by solving the bayesian conditional probability formula (2). The uncertainty u 1D of the neural network output Xn contains the uncertainty of the input and parameters.
The uncertainty of the data of the integrated network is obtained by averaging the standard deviation σ=u 1D of the output of each network conforming to the normal distribution, as shown in fig. 4 (a):
The uncertainty of the data is mainly caused by data noise, the confidence level is taken to be 95%, and the estimated value is taken Expressed as:
Finally, summing the model uncertainty and the data uncertainty as a total uncertainty, as shown in fig. 5;
ut＝um+uD (11)
although the uncertainty of the neural network and the uncertainty evaluation mode of the GUM have large differences and have no clear uncertainty propagation process, the actual uncertainty propagation is considered in the calculation of a probability density function, and the network integration method is utilized to consider the Bayesian theorem in the propagation process and the classical GUM method adopted in the uncertainty synthesis stage.
The above-described embodiments are merely preferred embodiments of the present invention, and are not intended to limit the present invention in any way. Any person skilled in the art will make many variations and modifications to the technical solution of the present invention using the technical content disclosed above without departing from the scope of the technical solution of the present invention, and the technical solution is equivalent to the present invention. Therefore, the equivalent changes according to the inventive concept should be covered in the protection scope of the present invention without departing from the technical scheme of the present invention.
Claims (5)
1. The method for evaluating the uncertainty of the dynamic measurement system based on the time sequence neural network is characterized by comprising the following steps of:
step S1, sample data acquisition, namely taking input data and output data of a dynamic measurement system as training data based on known model parameters and modeling processes of the dynamic measurement system;
Step S2, data processing is carried out, training data are preprocessed, each group of input data and corresponding output data are adjusted to be the same dimension and size, and time dimension slice reconstruction is carried out on long-sequence input signals;
step S3, modeling a neural network;
Two independent feedforward neural network structures are built in a single network, wherein one feedforward neural network structure is a neural network capable of processing time sequence information and is used for outputting an estimated value mean value x n; the other feedforward neural network is a linear feedforward neural network, and is used for outputting an estimated value variance sigma 2;
S4, loss function calculation and network training;
Calculating loss of the output x n and the true value x t of the neural network by adopting an MSE loss function, reversely transferring errors, carrying out optimization approximation by using a random gradient descent method, and training a single network by maximizing posterior distribution of an estimated mean value;
step S5, network integration;
And inputting the test data into a trained integrated network, and respectively quantifying the data uncertainty and the model uncertainty.
2. The method for assessing uncertainty of a dynamic measurement system based on a neural network of claim 1,
The step S1 specifically includes collecting M groups of dynamic time-related signals X 1、X2、X3...XM in batch, where each group of dynamic time-related signals have the same frequency, different peak values, and different time of occurrence of the peak values, and the input signal X t (t=1, 2,..n) serving as a dynamic measurement system is a function of time t, and the time sequence length is N;
under the input signal, the dynamic measurement system generates M sets of corresponding system output signals Y 1、Y2、Y3...YM, each set of output signals Y t (t=1, 2,.,. N); the output y t at each time t follows a normal distribution, with a probability density function of η t (t=1, 2, n.), the joint probability density function of the entire time sequence is encoded as The probability density function of the dynamic measurement system output sequence is:
Each set of input and output signals is matched as a sample dataset, with K (K < M) sets as training data and the remainder as test data.
3. The method for assessing uncertainty of a dynamic measurement system based on a neural network of claim 1,
In step S3, the inverse measurement process of the dynamic measurement system of step S1 is modeled using the neural network capable of processing the timing information, and the output signal y t of the dynamic measurement system is used as the input signal y n of the neural network (n=1, 2, n.), the neural network output x n (n=1, 2,.., N) is used as the input estimate value for the back-measurement dynamic measurement system, and the input signal x t of the step S1 dynamic measurement system is used as the output true value for the neural network.
4. The method for assessing uncertainty of a dynamic measurement system based on a neural network of claim 1,
The step S4 specifically comprises the following steps:
Since the output y t of the dynamic measurement system at each time t is subject to a normal distribution, the probability density function is η t (t=0, 1,2,..once., N), and the joint probability density function of the whole time sequence is encoded as The probability density function of the dynamic measurement system output
A data prior distribution P (y n) as a neural network;
(1) Calculating loss1 of x n and x t using the MSE function;
(2) According to the Bayesian theorem, the input and the output follow normal distribution, the input Y n and the theta are variables, the probability density function P (Y|X) in the step S1 is used as the known data prior distribution of the neural network input Y n, and a scheme of adding Gaussian noise to Y n is adopted to replace P (Y|X);
The neural network is modeled as:
P(xt|yn,θ)＝N(xt;xn,σ2) (2)
The objective is to obtain the estimated mean x n and variance σ 2 of the true value x t; likelihood function to maximize posterior prediction distribution:
Where N is the time series length, taking the negative value of the natural logarithm of the likelihood function as loss2:
the final total loss is:
loss＝loss1+loss2 (5)
Training is stopped when the sample is trained 1000 times or the gradient of the objective function is no longer reduced.
5. The method for evaluating uncertainty of dynamic measurement system based on time series neural network as set forth in claim 1, wherein,
The step S5 specifically comprises the following steps:
Inputting test data, storing the output of each network in step S5 and calculating the sample mean value And variance s 2:
model uncertainty is the overall variance:
The uncertainty of the model of the integrated method is represented by a confidence interval method according to GUM, the uncertainty of the model is mainly caused by the architecture of the model, the training process and the region with insufficient representativeness in training data, the confidence level is taken to be 95%, and the estimated value is taken Expressed as:
The uncertainty u 1D of the data output by the single network consists of two uncertainty components of the uncertainty u x of the input signal Yn and the uncertainty u θ of the network parameter theta, and the uncertainty propagation is realized by solving a Bayesian conditional probability formula (2);
the data uncertainty u 1D of the neural network output Xn contains the uncertainty of the input signal Yn and the network parameter θ;
the uncertainty of the data of the integrated network is obtained by averaging the standard deviation sigma=u 1D of the output of each network conforming to the normal distribution:
The uncertainty of the data is mainly caused by data noise, the confidence level is taken to be 95%, and the estimated value is taken Expressed as:
finally, summing the model uncertainty and the data uncertainty as a total uncertainty:
ut＝um+uD (11)。
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