A method for recovering continuous missing data based on multiple fusion interpolation

Abstract

The present invention discloses a method for recovering continuously missing data based on multiple fusion interpolation. First, a multi-rate asynchronous sampling multi-sensor model considering observation missing is established. In combination with the characteristics of multi-rate asynchronous measurement between sensors, the sensor monitoring data is divided in real time. Then, the missing state is recovered through one-step state prediction, multi-step state prediction, regression missing prediction and similar mean interpolation to obtain four types of recovery results. Finally, the fusion coefficient of the data to be recovered is calculated based on the maximum likelihood estimation evaluation criterion to obtain the fusion interpolation result of the missing data. The present invention solves the problem of continuous missing monitoring data caused by unfavorable factors such as sensor failure, communication delay, and transmission performance limitation in the prior art, establishes a continuous missing data recovery framework based on multiple fusion interpolation, and improves the accuracy of sensor state monitoring.

Description

Technical Field

[0001] The invention belongs to the technical field of information processing, and in particular relates to a method for recovering continuous missing data based on multiple fusion interpolation. Background Art

[0002] In recent years, thanks to the development of sensor technology, system status monitoring has become more convenient. Ideally, the monitoring results of the sensor should remain intact, but due to the combined influence of many factors such as the operating environment, sensor failure, communication delay, and transmission performance limitations, the monitoring data may not be obtained normally. In mild cases, a small amount of monitoring data may be intermittently missing, and in severe cases, a large amount of monitoring data may be continuously missing, which seriously affects the accuracy of system status monitoring. The development of advanced continuous missing data recovery theory research has broad application prospects and necessity. Summary of the invention

[0003] The purpose of the present invention is to provide a method for recovering continuously missing data based on multiple fusion interpolation, which solves the problem of continuous missing monitoring data caused by adverse factors such as sensor failure, communication delay, and transmission performance limitation in the prior art, establishes a continuous missing data recovery framework based on multiple fusion interpolation, and improves the accuracy of sensor status monitoring.

[0004] The technical solution adopted by the present invention is a method for recovering continuous missing data based on multiple fusion interpolation, which is specifically implemented according to the following steps:

[0005] Step 1: Establish a multi-rate asynchronous sampling multi-sensor model that takes into account observation missing, and divide the sensor monitoring data in real time based on the characteristics of multi-rate asynchronous measurement between sensors;

[0006] Step 2: Recover the missing state through one-step state prediction, multi-step state prediction, regression missing prediction and similar mean interpolation to obtain four types of recovery results;

[0007] Step 3: Calculate the fusion coefficient of the data to be restored based on the maximum likelihood estimation evaluation criterion to obtain the fusion interpolation result of the missing data.

[0008] The present invention is also characterized in that:

[0009] Step 1 is implemented according to the following steps:

[0010] Step 1.1: Establish the following multi-rate asynchronous sampling multi-sensor measurement model considering observation missing:

[0011] v (k+1)T =f(v kT )+w kT ,k=1,2,3,…

[0012]

[0013] In the formula, i is the serial number of the sensor, there are L sensors in total, among which, v kT is the system state at time kT, T is the state update period, k is the system state update point number, n (i) is the sampling period multiplier of the i-th sensor observation, n (i) T is the observation sampling period, where n (i) ≥1 is a positive integer, For the system in n (i) The measurement result of the i-th sensor at time kT, n (i) The system state at time kT, w kT and are state noise and observation noise, with variances Q and R respectively (i) , f(·) is the nonlinear state function of the system, which indicates the changing characteristics of the system under different operation modes, h (i) (·) represents the measurement function of the i-th sensor, is the i-th sensor n (i) The system state coefficient at time kT is (i) kT has measurement results at the current moment, is 1, otherwise it is 0;

[0014] Step 1.2: Set the number of state points contained in each data block to N B , whenever the number of system state updates reaches N B Then these N B The state update points and the corresponding sensor measurement data are divided into a data block, and the size of each data block is N B for:

[0015] N B =[n (1) ,n (2) ,…,n (i) ]

[0016] i=1,2,…,L

[0017] In the formula, [·] represents the operation of finding the least common multiple, n (i) represents the sampling period multiplier of the i-th sensor observation;

[0018] Step 1.3: Classify the divided data blocks. If data missing occurs continuously in two or more data blocks, it is determined that there is a continuity loss of the monitoring data.

[0019] Step 2 is implemented as follows:

[0020] Step 2.1: For the continuous data missing in multiple data blocks, set the Nth b The missing data in the data blocks need to be restored. In the one-step state prediction, the previous data block, i.e., the Nth b The local state estimation result at the end of the -1 data block is used as the iteration starting point, and the Nth b The missing data in the Nth data block are restored in sequence. If the continuous missing data has not stopped, b Repeat the above steps for +1 data blocks until all the consecutive missing data are recovered:

[0021]

[0022] In the formula, is the i-th sensor n (i) The local estimation result obtained by the Kalman filter at time kT is: For the next moment, that is, n (i) The sensor missing data recovery result obtained at time (k+1)T, h (i) (·) represents the measurement function of the ith sensor, and f(·) is the nonlinear state function of the system;

[0023] Step 2.2: In multi-step state prediction, let the Nth b The missing data in the data block needs to be restored, and the previous data block, that is, the Nth b -1 The local state estimation result at the end of the data block is used as the measurable point, and the Nth b The missing data in the Nth data block are restored in sequence. If the continuous missing data has not stopped, b Repeat the above steps for +1 data blocks until all the consecutive missing data are recovered:

[0024]

[0025] In the formula, is the i-th sensor n (i) The measurement data recovery result at (k+m)T time, is the one-step prediction result obtained by Kalman filter estimation based on the previous measurement moment, is the missing data interpolation result based on multi-step prediction, f [m] (·) means f(·) is iterated and run m times;

[0026] Step 2.3: Select univariate linear regression in regression prediction to predict the missing measurement. Let N b The missing data in the Nth data block needs to be restored. b-1 The continuous missing phenomenon in the data block appears in the Nth b data blocks, based on the Nth b -1 data block to calculate the regression correlation coefficient, assuming that the Nth sensor of the i-th sensor b - Measurement results in 1 data block for:

[0027]

[0028] Based on the following formula, b Predict missing observations in blocks of data:

[0029]

[0030] In the formula, for The restored value of the mth observation point after is the regression coefficient, is the error term, and The calculation of is as follows:

[0031]

[0032]

[0033]

[0034]

[0035] In the formula, is the average value at the sampling time, is the average value of the measurement results. is restored, it is combined with the updated Combining, we get:

[0036]

[0037] Corresponding to the updated Recalculate and Get the recovery value at the next measurement time, and iterate until all missing data in the current data block are recovered. If the Nth b +1 data block still has missing data, then based on the Nth b Measurement data in blocks Continue to recover according to the above iterative process until all missing data are recovered;

[0038] Step 2.4: In the same type of mean interpolation, the average value of the measurement results of different sensors of the same type at the same time is selected as the recovery value of the missing data. Let n (i) The missing measurement of the ith sensor at time kT Need to be restored, the restoration result is obtained by the following formula:

[0039]

[0040] Step 3 is implemented as follows:

[0041] Step 3.1: Assume that the measurement data to be restored at the current moment is The four types of restored data obtained in step 2 are defined as one-step state prediction Multi-step state prediction Regression state prediction and similar mean interpolation

[0042] Step 3.2: Set the difference between the current measurement time to be restored and the last continuous loss end time moment, the measurement vector between these two moments Written as:

[0043]

[0044] Calculate the measurement results corresponding to the global fusion estimate As shown below:

[0045]

[0046] make and The error vector ε between (i) for:

[0047]

[0048] Step 3.3: Estimate the mean of the initial error vector based on maximum likelihood estimation, as shown in the following formula:

[0049]

[0050]

[0051] In the formula, is the joint probability density function, is the maximum likelihood estimation result of the mean of the original error vector;

[0052] Step 3.4: Repeat step 3.3 for and The mean of the new information measurement vector error is estimated, which are and make

[0053]

[0054]

[0055] Get the fusion recovery weight corresponding to each prediction result and As shown below:

[0056]

[0057] Step 3.5: Based on the above steps, n (i) kT time to restore the measurement data The fusion interpolation result is obtained by the following formula:

[0058]

[0059] Step 3.6: When recovering the missing values ​​at the next moment, include The initial error vector is calculated based on the measurement data including the restored value, and steps 3.2-3.6 are repeated until the fusion interpolation result at that moment is obtained, and so on, until all the missing data are restored.

[0060] The beneficial effect of the present invention is that a method for recovering continuous missing data based on multiple fusion interpolation is established, taking into account that the sampling rates, measurement mechanisms and observation functions of each sensor are different in the actual measurement process, and a multi-rate asynchronous sampling multi-sensor model considering observation missing is established. In combination with the characteristics of multi-rate asynchronous measurement between sensors, the sensor monitoring data is divided in real time; the missing state is restored through one-step state prediction, multi-step state prediction, regression missing prediction and similar mean interpolation to obtain four types of recovery results; the fusion coefficient is calculated based on the maximum likelihood estimation evaluation criterion to obtain the fusion interpolation result of the missing data. The algorithm has good missing data recovery effect and high precision, and has strong reference and practicality. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 It is a missing data recovery structure block diagram of a continuous missing data recovery method based on multiple fusion interpolation of the present invention;

[0062] Figure 2 It is a missing data recovery result diagram of a continuous missing data recovery method based on multiple fusion interpolation of the present invention. DETAILED DESCRIPTION

[0063] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0064] The present invention provides a method for recovering continuous missing data based on multiple fusion interpolation, the flow chart of which is as follows: Figure 1 As shown, the specific implementation steps are as follows:

[0065] Step 1: Considering that the sampling rate, measurement mechanism and observation function of each sensor are different in the actual measurement process, a multi-rate asynchronous sampling multi-sensor model considering observation missing is established, and the sensor monitoring data is divided in real time based on the characteristics of multi-rate asynchronous measurement between sensors;

[0066] Step 1 is implemented according to the following steps:

[0067] Step 1.1: Establish the following multi-rate asynchronous sampling multi-sensor measurement model considering observation missing:

[0068] v (k+1)T =f(v kT )+w kT ,k=1,2,3,…

[0069]

[0070] In the formula, the system state is updated uniformly. In each state update cycle, each sensor samples at most once. i is the serial number of the sensor, and there are L sensors in total. Among them, v kT is the system state at time kT, T is the state update period, k is the system state update point number, n (i) is the sampling period multiplier of the i-th sensor observation, n (i) T is the observation sampling period, where n (i) ≥1 is a positive integer, For the system in n (i) The measurement result of the i-th sensor at time kT, n (i) The system state at time kT, w kT and They are state noise and observation noise, which are uncorrelated zero-mean Gaussian white noises with variances Q and R respectively. (i) , f(·) is the nonlinear state function of the system, which indicates the changing characteristics of the system under different operation modes, h (i) (·) represents the measurement function of the i-th sensor, is the i-th sensor n (i) The system state coefficient at time kT is (i) kT has measurement results at the current moment, is 1, otherwise it is 0;

[0071] Step 1.2: Considering the characteristics of multi-rate asynchronous measurement between sensors, the number of state points contained in each data block is set to N. B , whenever the number of system state updates reaches N B Then these N B The state update points and the corresponding sensor measurement data are divided into a data block, and the size of each data block is N B for:

[0072] N B =[n (1) ,n (2) ,…,n (i) ]

[0073] i=1,2,…,L

[0074] In the formula, [·] represents the operation of finding the least common multiple, n (i) represents the sampling period multiplier of the i-th sensor observation;

[0075] Step 1.3: Classify the divided data blocks. If data missing occurs continuously in two or more data blocks, it is determined that there is a continuity loss of the monitoring data.

[0076] Step 2: Recover the missing state through one-step state prediction, multi-step state prediction, regression missing prediction and similar mean interpolation to obtain four types of recovery results;

[0077] Step 2 is implemented as follows:

[0078] Step 2.1: For the continuous data missing in multiple data blocks, set the Nth b The missing data in the data blocks need to be restored. In the one-step state prediction, the previous data block, i.e., the Nth b The local state estimation result at the end of the -1 data block is used as the iteration starting point, and the Nth b The missing data in the Nth data block are restored in sequence. If the continuous missing data has not stopped, b Repeat the above steps for +1 data blocks until all the consecutive missing data are recovered:

[0079]

[0080] In the formula, is the i-th sensor n (i) The local estimation result obtained by the Kalman filter at time kT is: For the next moment, that is, n (i) The sensor missing data recovery result obtained at time (k+1)T, h (i)(·) represents the measurement function of the ith sensor, and f(·) is the nonlinear state function of the system;

[0081] Step 2.2: In multi-step state prediction, let the Nth b The missing data in the data block needs to be restored, and the previous data block, that is, the Nth b -1 The local state estimation result at the end of the data block is used as the measurable point, and the Nth b The missing data in the Nth data block are restored in sequence. If the continuous missing data has not stopped, b Repeat the above steps for +1 data blocks until all the consecutive missing data are recovered:

[0082]

[0083] In the formula, is the i-th sensor n (i) The measurement data recovery result at (k+m)T time, is the one-step prediction result obtained by Kalman filter estimation based on the previous measurement moment, is the missing data interpolation result based on multi-step prediction, f [m] (·) means f(·) is iterated and run m times;

[0084] Step 2.3: Select univariate linear regression in regression prediction to predict the missing measurement. Let N b The missing data in the Nth data block needs to be restored. b -1 The continuous missing phenomenon in the data block appears in the Nth b data blocks, based on the Nth b -1 data block to calculate the regression correlation coefficient, assuming that the Nth sensor of the i-th sensor b - Measurement results in 1 data block for:

[0085]

[0086] Based on the following formula, b Predict missing observations in blocks of data:

[0087]

[0088] In the formula, for The restored value of the mth observation point after is the regression coefficient, is the error term, and The calculation of is as follows:

[0089]

[0090]

[0091]

[0092]

[0093] In the formula, is the average value at the sampling time, is the average value of the measurement results. is restored, it is combined with the updated Combining, we get:

[0094]

[0095] Corresponding to the updated Recalculate and Get the recovery value at the next measurement time, and iterate until all missing data in the current data block are recovered. If the Nth b +1 data block still has missing data, then based on the Nth b Measurement data in blocks Continue to recover according to the above iterative process until all missing data are recovered;

[0096] Step 2.4: In the same type of mean interpolation, the average value of the measurement results of different sensors of the same type at the same time is selected as the recovery value of the missing data. Let n (i) The missing measurement of the ith sensor at time kT Need to be restored, the restoration result is obtained by the following formula:

[0097]

[0098] Step 3: Calculate the fusion coefficient of the data to be restored based on the maximum likelihood estimation evaluation criterion to obtain the fusion interpolation result of the missing data.

[0099] Step 3 is implemented as follows:

[0100] Step 3.1: Assume that the measurement data to be restored at the current moment is The four types of restored data obtained in step 2 are defined as one-step state prediction Multi-step state prediction Regression state prediction and similar mean interpolation

[0101] Step 3.2: Set the difference between the current measurement time to be restored and the last continuous loss end time moment, the measurement vector between these two moments Written as:

[0102]

[0103] Calculate the measurement results corresponding to the global fusion estimate As shown below:

[0104]

[0105] make and The error vector ε between (i) for:

[0106]

[0107] Step 3.3: Estimate the mean of the initial error vector based on maximum likelihood estimation, as shown in the following formula:

[0108]

[0109]

[0110] In the formula, is the joint probability density function, is the maximum likelihood estimation result of the mean of the original error vector;

[0111] Step 3.4: Repeat step 3.3 for and The mean of the new information measurement vector error is estimated, which are and make

[0112]

[0113]

[0114] Get the fusion recovery weight corresponding to each prediction result and As shown below:

[0115]

[0116] Step 3.5: Based on the above steps, n (i) kT time to restore the measurement data The fusion interpolation result is obtained by the following formula:

[0117]

[0118] Step 3.6: When recovering the missing values ​​at the next moment, include The initial error vector is calculated based on the measurement data including the restored value, and steps 3.2-3.6 are repeated until the fusion interpolation result at that moment is obtained, and so on, until all the missing data are restored.

[0119] Figure 2 This is the missing data recovery result diagram of the present invention. In the figure, the black solid line is the real state value of a system, the dotted line is the sensor monitoring state value, and the black dotted solid line is the missing data recovery value. Figure 2 It can be clearly seen from the observation that the method proposed in the present invention can effectively recover the system's continuously missing data, and the overall trend of the recovered data is consistent with the actual change state of the system.

Claims

1. A method for recovering continuous missing data based on multiple fusion interpolation, characterized in that: Follow the steps below to implement it: Step 1: Establish a multi-rate asynchronous sampling multi-sensor model that takes into account observation missing, and divide the sensor monitoring data in real time based on the characteristics of multi-rate asynchronous measurement between sensors; The step 1 is specifically implemented according to the following steps: Step 1.1: Establish the following multi-rate asynchronous sampling multi-sensor measurement model considering observation missing: v (k+1)T =f(v kT )+w kT ,k=1,2,3,… In the formula, i is the serial number of the sensor, there are L sensors in total, among which, v kT is the system state at time kT, T is the state update period, k is the system state update point number, n (i) is the sampling period multiplier of the i-th sensor observation, n (i) T is the observation sampling period, where n (i) ≥1 is a positive integer, For the system in n (i) The measurement result of the i-th sensor at time kT, n (i) The system state at time kT, w kT and are state noise and observation noise, with variances Q and R respectively (i) , f(·) is the nonlinear state function of the system, which indicates the changing characteristics of the system under different operation modes, h (i) (·) represents the measurement function of the i-th sensor, is the i-th sensor n (i) The system state coefficient at time kT is (i) kT has measurement results at the current moment, is 1, otherwise it is 0; Step 1.2: Set the number of state points contained in each data block to N B , whenever the number of system state updates reaches N B Then these N B The state update points and the corresponding sensor measurement data are divided into a data block, and the size of each data block is N B for: N B =[n (1) ,n (2) ,…,n (i) ] i=1,2,…,L In the formula, [·] represents the operation of finding the least common multiple, n (i) represents the observation sampling period multiplier of the i-th sensor; Step 1.3: Classify the divided data blocks. If the data missing situation appears in two or more data blocks continuously, it is determined that the monitoring data is missing continuously. Step 2: Recover the missing state through one-step state prediction, multi-step state prediction, regression missing prediction and similar mean interpolation to obtain four types of recovery results; The step 2 is specifically implemented according to the following steps: Step 2.1: For the continuous data missing in multiple data blocks, set the Nth b The missing data in the data blocks need to be restored. In the one-step state prediction, the previous data block, i.e., the Nth b The local state estimation result at the end of the -1 data block is used as the iteration starting point, and the Nth b The missing data in the Nth data block are restored in sequence. If the continuous missing data has not stopped, b Repeat the above steps for +1 data blocks until all the consecutive missing data are recovered: In the formula, is the i-th sensor n (i) The local estimation result obtained by the Kalman filter at time kT is: For the next moment, that is, n (i) The sensor missing data recovery result obtained at time (k+1)T, h (i) (·) represents the measurement function of the ith sensor, and f(·) is the nonlinear state function of the system; Step 2.2: In multi-step state prediction, let the Nth b The missing data in the data block needs to be restored, and the previous data block, that is, the Nth b -1 The local state estimation result at the end of the data block is used as the measurable point, and the Nth b The missing data in the Nth data block are restored in sequence. If the continuous missing data has not stopped, b Repeat the above steps for +1 data blocks until all the consecutive missing data are recovered: In the formula, is the i-th sensor n (i) The measurement data recovery result at (k+m)T time, is the one-step prediction result obtained by Kalman filter estimation based on the previous measurement moment, is the missing data interpolation result based on multi-step prediction, f [m] (·) means f(·) is iterated and run m times; Step 2.3: Select univariate linear regression in regression prediction to predict the missing measurement. Suppose the Nth b The missing data in the Nth data block needs to be restored. b -1 The continuous missing phenomenon in the data block appears in the Nth b data blocks, based on the Nth b -1 data block to calculate the regression correlation coefficient, assuming that the Nth sensor of the i-th sensor b - Measurement results in 1 data block for: Based on the following formula, b Predict missing observations in blocks of data: In the formula, for The restored value of the mth observation point after is the regression coefficient, is the error term, and The calculation of is as follows: In the formula, is the average value at the sampling time, is the average value of the measurement results. is restored, it is combined with the updated Combining, we get: Corresponding to the updated Recalculate and Get the recovery value at the next measurement time, and iterate until all missing data in the current data block are recovered. If the Nth b +1 data block still has missing data, then based on the Nth b Measurement data in blocks Continue to recover according to the above iterative process until all missing data are recovered; Step 2.4: In the same type of mean interpolation, the average value of the measurement results of different sensors of the same type at the same time is selected as the recovery value of the missing data. Let n (i) The missing measurement of the ith sensor at time kT Need to be restored, the restoration result is obtained by the following formula: Step 3: Calculate the fusion coefficient of the data to be restored based on the maximum likelihood estimation evaluation criterion to obtain the fusion interpolation result of the missing data; The step 3 is specifically implemented according to the following steps: Step 3.1: Assume that the measurement data to be restored at the current moment is The four types of restored data obtained in step 2 are defined as one-step state prediction Multi-step state prediction Regression state prediction and similar mean interpolation Step 3.2: Assume that the difference between the current measurement time to be restored and the last continuous loss end time is n (i) T moments, the measurement vector between these two moments Written as: Calculate the measurement results corresponding to the global fusion estimate As shown below: make and The error vector ε between (i) for: Step 3.3: Estimate the mean of the initial error vector based on maximum likelihood estimation, as shown in the following formula: In the formula, is the joint probability density function, is the maximum likelihood estimation result of the mean of the original error vector; Step 3.4: Repeat step 3.3 for and The mean of the new information measurement vector error is estimated, which are and make Get the fusion recovery weight corresponding to each prediction result and As shown below: Step 3.5: Based on the above steps, n (i) kT time to restore the measurement data The fusion interpolation result is obtained by the following formula: Step 3.6: When recovering the missing values ​​at the next moment, include The initial error vector is calculated based on the measurement data including the restored value, and steps 3.2-3.6 are repeated until the fusion interpolation result at that moment is obtained, and so on, until all the missing data are restored.

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