CN112763225A - Sensor error identification and elimination method based on Laplace feature mapping algorithm - Google Patents

Sensor error identification and elimination method based on Laplace feature mapping algorithm Download PDF

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CN112763225A
CN112763225A CN202011562623.XA CN202011562623A CN112763225A CN 112763225 A CN112763225 A CN 112763225A CN 202011562623 A CN202011562623 A CN 202011562623A CN 112763225 A CN112763225 A CN 112763225A
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张淼
詹译傲
任江航
耿振亚
王艳
沈毅
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    • G—PHYSICS
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Abstract

A sensor error identification and elimination method based on a Laplace feature mapping algorithm relates to the field of engine testing, and continuous and accurate measurement of engine temperature is completed by adopting an annular symmetrical temperature measurement structure, Laplace feature mapping and a wavelet-based denoising algorithm. The method comprises the following steps: firstly, in order to deal with the airflow disturbance generated by deflection of the tail flame of the engine, a measuring device with an annular symmetrical structure of an engine combustion chamber is arranged. And secondly, in order to effectively weaken and remove the measurement interference in time, the target temperature value is obtained through further dimension reduction processing by a Laplace characteristic mapping algorithm. And finally, performing sensor temperature signal denoising processing through wavelet transform filtering, and selecting a wavelet basis Coif5 to perform temperature signal denoising processing to eliminate measurement errors caused by complex temperature change rules of the tail flame of the engine. The invention can effectively solve the problems of poor temperature measurement accuracy caused by complex temperature change rules and difficulty in timely and effective removal of measurement interference.

Description

Sensor error identification and elimination method based on Laplace feature mapping algorithm
Technical Field
The invention relates to a sensor error identification and elimination method, in particular to a Laplace feature mapping algorithm.
Background
The development of the engine generally needs ground test verification, and finally flight test assessment is carried out, the types of test beds are various, wherein the wind tunnel test is a test mode only second to the flight test, the working state of the engine is simulated more truly, but the air consumption is large, the consumption is high, the dependence on energy is large, and the wind tunnel test is not suitable for a large number of tests. The test bed can provide all conditions required by the actual operation of the engine, can adjust the parameters of the air inlet, the air exhaust, the fuel flow, the pressure, the temperature and the like of the engine to the same data as those in the flight process, collects the internal temperature, the pressure change, the thrust, the vibration, the rotating speed and other state changes of the engine under different working conditions, and the changes of the engine accessories, such as the output voltage and the current of a generator, and evaluates whether the engine meets the design indexes or not by analyzing the data, so the performance of the engine test bed and the advancement of the ground test technology of the engine are the prerequisite conditions for developing a high-quality engine, and the precision of the test bed is derived from the precision of a measurement and control system.
The measurement and control system of the test bed of the small aircraft and the missile engine has the annular characteristic, the height of the measurement ring is coaxial with the engine, and the measurement ring is arranged far in front of the engine in the air inlet direction and used for measuring the total air inlet pressure and the total air inlet temperature of the engine. In order to accurately obtain the total temperature value of the current position, a plurality of branch thermal resistance temperature sensors are used for measuring, finally, an average value is taken to represent the current total temperature value, and an annular distribution measurement mode is adopted.
In engineering, an engine tail nozzle can be generally used as a cavity, the area of the cavity is the same as that of a tail nozzle opening, the cavity can change along with the change of the state of an engine, tail flames are axisymmetric, the area of the cavity is the same as that of the tail nozzle opening, the tail flames can be divided into a core area and a mixing area according to the change situation of the temperature of the tail flames, the temperature of the core area is basically constant, the temperature is high, the core area is the main part of infrared radiation, and the temperature of the mixing area is low.
The emissivity of the tail flame of the engine is closely and complexly related to the material, the surface state, the wavelength and the temperature of the tail flame, the plume of the tail flame of the engine is a complex plasma field of two-phase flow of a gas phase and a condensed phase, the emissivity of the plume can change along with the change of decomposition products, the temperature and the like of a combustion state over time, and the accurate numerical value of the emissivity is difficult to obtain, which is the characteristic of the plume field and is also a difficult point in the temperature measurement technology.
The thermal infrared imager is commonly used in engineering for measuring the temperature of the plume of the tail flame of an engine, the emissivity of any position of an plume field in the working period of the engine at any time is generally regarded as the same constant, the influence of time-domain change of the emissivity on the accuracy of a measurement result cannot be eliminated, the emissivity of the plume field of the engine is difficult to obtain in real time, the temperature of the plume field is changed quickly, the tail flame at the outlet of a combustion chamber can deflect, the accuracy of the temperature measurement result is poor, and the thermal infrared imager has the defect that the temperature measurement cannot be avoided and cannot be overcome in the application process of the existing thermal.
The Laplacian eigenmap algorithm (LE) is a method for constructing the relationship between data from the perspective of local approximation, and LE is a dimension reduction algorithm based on a graph, which constructs data to be dimension reduced into the graph, and each node of the graph and the node closest to the node establish an edge relationship, and then it expects the points connected in the graph (the points close to each other in the original space) to be as close as possible in the space after dimension reduction, so that the original local structural relationship can be maintained after dimension reduction.
Disclosure of Invention
The invention aims to overcome the defects that the temperature measurement accuracy is poor and the measurement interference is not timely and effectively weakened and removed due to the complex temperature change rule of the traditional temperature sensor. In order to solve the problem of poor temperature measurement accuracy caused by complex temperature change rules, an annular temperature measurement structure is designed to timely and effectively weaken and remove measurement interference, wavelet transform filtering is adopted to perform noise reduction processing on a sensor temperature signal, and a sensor temperature measurement error based on a Laplace characteristic mapping algorithm is eliminated based on the problems, so that the accuracy of a measurement and control system of an engine test bed is accurately improved.
The purpose of the invention is realized by the following technical scheme: the method comprises the steps of firstly arranging an engine combustion chamber outlet temperature field measuring device to be of an annular symmetrical structure, measuring by using a plurality of thermal resistance temperature sensors for multiple times, taking an average value, carrying out multiple processes together, and obtaining a field of data points. Then, a weight matrix is created to be a thermal kernel function, then characteristic decomposition is carried out, then the dimension reduction process is expanded from one dimension to multiple dimensions to obtain a target function of an LE algorithm, and then filtering processing is carried out on the low-frequency oscillation signals of the sensor data by using a new noise reduction processing method of wavelet transform filtering, so that an accurate result of the temperature measured by the instantaneous temperature sensor is obtained, and the accuracy of a measurement and control system of the engine test bed is improved.
The flow chart of the implementation of the invention is shown in figure 1, and is divided into three steps, and the specific steps are as follows:
the method comprises the following steps: the temperature measuring device adopts an annular symmetrical temperature measuring structure which is uniformly distributed, and the problem that the temperature measuring accuracy is not high due to the complex temperature change rule can be effectively solved.
The device for measuring the temperature field of the outlet of the combustion chamber of the engine is arranged to be of an annular symmetrical structure, the height of the measuring ring is coaxial with the engine, and the measuring ring is arranged far in front of the air inlet direction of the engine and used for measuring the total air inlet pressure and the total air inlet temperature of the engine; in order to accurately obtain the total temperature value of the current position, a plurality of branch thermal resistance temperature sensors are used for measuring, and finally, the average value is obtained through multiple times of measurement; the temperature measuring device adopts an annular distribution measuring mode, and a plurality of sensors are dispersedly arranged on the same cross section in the mode, so that the measuring margin is increased, the measuring points are uniformly distributed, and the result is more accurate.
The invention considers the factor of airflow disturbance at the assembly position of the sensor, and for the sensor, on the premise of ensuring the consistency of the temperature sensing element (such as the packaging position of a thermal resistor, the packing density, the position of a thermal resistor wire winding and the like), the symmetry of the assembly position of the temperature sensing element relative to a tail flame port needs to be improved, if the tail flame at the outlet of a combustion chamber deflects, the distribution of the airflow inside the sensor is biased, so that the airflow flowing through the temperature sensing element of the sensor is different, the two paths of response time of the sensor are inconsistent, and the two paths of temperature sensing elements of the sensor need to be symmetrical left and right relative to the tail flame port. Under the dynamic condition, the temperature in the stagnation cavity of the sensor is gradient, if the positions of the thermal resistors in the two paths of temperature sensing elements in the axial direction are different, the temperature sensed by the thermal resistors in the temperature change process is also different, so that the response time is inconsistent, and therefore the two paths of temperature sensing elements of the sensor, particularly the internal thermal resistors, need to be vertically symmetrical relative to the tail flame opening.
Step two: and processing by a Laplace characteristic mapping algorithm to obtain a target temperature value.
First, a raw data set X ═ X is created for the measured temperature1,x2,...,xN]∈RD×NWherein D is the data dimension, N is the number of samples, the number of near neighborhoods and the dimension reduction dimension D are set, and t belongs to RD×N(ii) a Finding out the neighborhood, creating neighborhood graph G, and searching each sample X by k-nearest neighbor methodiThe most recent k samples
Figure BDA0002859780330000031
The connection line of the two adjacent points is the edge in the neighborhood graph G; the calculation of G comprises two steps of neighbor selection and weight calculation; firstly, a field of data points is obtained by measuring by using a plurality of thermal resistance temperature sensors, then weights are defined for all edges, and a weight matrix of high-dimensional spatial data is constructed as follows:
Figure BDA0002859780330000032
then, a weight matrix is established to be a thermal kernel function, and then characteristic decomposition is carried out:
Lz＝λDz
wherein, the laplacian matrix L is D-W, D is the degree matrix, D is diag { D ═ D1,d2,d3,...,dN}，diIs a proximity matrix
Figure BDA0002859780330000033
For the case of one-dimensional reduction, the objective function of the LE algorithm is:
Figure BDA0002859780330000034
wherein (C)TIs a transpose of a matrix, WijHas a value of xiAnd xjThe greater the weight between, x is showniAnd xjThe more similar, if WijIs very large, according to the constraint of the above formula, yi-yjApproaching 0, i.e. and high-dimensional data point xiAnd xjCorresponding low dimensional data yiAnd yjThe method is also very similar, so that the local adjacency relation of the data before and after dimension reduction is kept, and P is a constant vector of m dimension; taking the value of P as 1, through simplification and optimization of an objective function, the solution of the above formula is converted into the solution of the generalized eigenvalue of the following formula. Where λ is the eigenvalue, the dimensionality reduction result y*That is, the feature vector corresponding to the minimum non-0 feature value, namely:
Ly＝λDy
the dimension reduction process is expanded from one dimension to multiple dimensions, and the objective function of the LE algorithm is expressed as follows:
y*＝argmintr(YLYT)
wherein tr () is the matrix tracing operation, the dimensionality reduction data y at this time*For m minimum eigenvectors corresponding to non-0 eigenvalues, the value of m is suggested to be [1,5 ]]Finally obtaining the final temperature value
Figure BDA0002859780330000035
In degrees celsius.
Step three: because the temperature change rule of the tail flame of the engine is complex, the temperature measurement data inevitably has errors, finally, the noise reduction processing of the temperature signal of the sensor is carried out through wavelet transform filtering, and the noise reduction effect is best when the wavelet basis is Coif5 through the experimental analysis of the important contrast wavelet basis, namely Coif1, Coif2, Coif3, Coif4, Coif5 and other typical wavelet basis, therefore, the invention selects Coif5 to carry out filtering processing on the low-frequency signal of the temperature measurement data on the wavelet basis, thereby greatly overcoming the distortion problem of the traditional Fourier transform signal, producing smooth attenuation curve, effectively removing noise and keeping the characteristics of the original signal.
The basic idea of wavelet threshold denoising is to set a critical threshold, compare the wavelet coefficient with the critical threshold, if less than, the coefficient is mainly caused by noise, and eliminate the coefficient; if the coefficient is larger than the critical threshold value, the coefficient is mainly caused by signals, the part of the coefficient is left, and then the wavelet inverse transformation is carried out on the processed wavelet coefficient to obtain the de-noised signals.
The wavelet denoising method comprises the following steps: wavelet transform is carried out on the signal f (t) with noise to obtain a group of wavelet decomposition coefficients Wj,kBy decomposing the wavelet coefficients Wj,kPerforming threshold processing to obtain estimated wavelet coefficient
Figure BDA0002859780330000041
Make it
Figure BDA0002859780330000042
Using estimated wavelet coefficients as small as possible
Figure BDA0002859780330000043
And performing wavelet reconstruction to obtain an estimated signal f (t), namely the denoised signal.
Aiming at the difficulty of fast and accurate extraction of wavelet coefficients in wavelet denoising, a very simple method is provided for wavelet coefficients Wj,kAnd (6) estimating. After wavelet decomposition is continuously carried out on f (t) for several times, a space distribution non-uniform signal C (k) is provided, and wavelet coefficients W on all scales are obtainedj,kHaving larger values at certain specific locations, which correspond to odd locations and important information of the original signal C (k)And W at most other positionsj,kSmaller, for white noise, its corresponding wavelet coefficient Wj,kThe distribution is uniform at each scale and W increases with the scalej,kThe magnitude of the coefficient decreases. Therefore, the general denoising method is to find a suitable number as a threshold value and apply a wavelet function W below the critical threshold valuej,kSet to zero and for wavelet functions W abovej,kThen the wavelet coefficients are retained or shrunk to obtain the estimated wavelet coefficients
Figure BDA0002859780330000044
It is understood to be essentially caused by the signal C (k), then
Figure BDA0002859780330000045
The original signal can be reconstructed by performing the reconstruction.
The invention processes the discrete time series X of noisy temperature data by LE algorithmn(t) continuous wavelet transform:
Figure BDA0002859780330000046
Figure BDA0002859780330000047
wherein, the theta number represents complex conjugate, s is resolution scale, t is time, n is time translation amount, delta t is time transformation amount, psi is mother wavelet psi0The non-dimensionalized result is calculated by the step to finally obtain the temperature signal data required by the invention, and a smooth data curve is formed.
Compared with the prior art, the invention has the following advantages:
the invention adopts a symmetrical temperature measurement structure with annular uniform distribution for the temperature measurement mode, and the mode dispersedly arranges a plurality of sensors on the same cross section, increases the measurement margin and simultaneously achieves uniform distribution of the measurement points, so that the result is more accurate, the problem of low temperature measurement accuracy caused by complex temperature change rules can be effectively solved, and the temperature data of the tail flame of the engine can be accurately measured.
Meanwhile, a Laplace characteristic mapping algorithm is adopted, a weight matrix is created to be a thermal kernel function, characteristic decomposition is carried out, the dimension reduction process is expanded from one dimension to multiple dimensions, a target function of an LE algorithm is obtained, measurement interference is timely and effectively weakened and removed, the method can process large-scale and noisy multi-channel temperature signals, therefore, the method has obvious advantages in the aspect of processing the multi-channel temperature signals, the method is superior to other dimension reduction methods in the aspects of accuracy and measurement interference resistance, and the method considers that the Laplace characteristic mapping has low calculation complexity, so the method has obvious advantages in the aspect of running time consumption.
Finally, according to temperature signal data, wavelet basis Coif5 is selected to perform noise reduction processing on the temperature signal of the sensor to eliminate the complex change rule of the temperature of the tail flame of the engine, and inevitable errors exist in temperature measurement data.
Drawings
FIG. 1 is a flow chart of the present invention.
FIG. 2 is a "0-0" cross-section total temperature and pressure measurement loop.
Fig. 3 is a flow chart of a laplacian feature mapping algorithm implementation.
Fig. 4 is a graph of temperature data after wavelet transform.
Detailed Description
The following description of the embodiments of the present invention is made with reference to the accompanying drawings and examples:
the test bed uses platinum as a temperature sensing element of the sensor, the figure 2 is an axial view of a measuring ring, the precision of the test bed can reach A-level tolerance and the like (0.15 +/-0.003 t ℃), the temperature coverage range of the platinum resistance sensor is-200-400 ℃, the size of a shell of the sensor is designed according to the size of a pipeline, the pressure of a measuring point and the flow rate of the measuring point, the platinum resistance is placed in the shell, and the error caused by a lead wire can be reduced by using a three-wire lead-out wire.
Executing the step one: taking a full-temperature and full-pressure measuring ring with a section of 0-0 of the engine as an example, fig. 2 is an axial view of the measuring ring, the height of the measuring ring is coaxial with the engine, and the measuring ring is arranged far in front of the air inlet direction of the engine and used for measuring the total air inlet pressure and the total air inlet temperature of the engine.
In the examples, 6 measurements of the thermal resistance temperature sensor were used, and the final measurement was averaged 3 times for a total of 6 runs. In the figure 2, Ttnij 1-Ttnij 6 adopt an annular distribution measurement mode, and a plurality of sensors are dispersedly arranged on the same cross section in the mode, so that the measurement margin is increased, and the measurement points are uniformly distributed, so that the result is more accurate.
And (5) executing the step two: first, a raw data set X ═ X is created for the measured temperature1,x2,...,xN]∈RD×NWherein D is the data dimension, N is the number of samples, the number of near neighborhoods and the dimension reduction dimension D are set, and t belongs to RD×NFinding out the neighborhood, creating a neighborhood graph G, and searching each sample X by a k-nearest neighbor methodiThe most recent k samples
Figure BDA0002859780330000051
The line connecting two adjacent points is the edge in the neighborhood graph G. The calculation of G comprises two steps of neighbor selection and weight calculation, namely, firstly, a field of data points is obtained by measuring through a plurality of thermal resistance temperature sensors, then weights are defined for all edges, a weight matrix of high-dimensional space data is constructed, then the weight matrix is created to be a thermonuclear function, and then characteristic decomposition is carried out, wherein a Laplace matrix L is D-W, D is a degree matrix, and W is an adjacent matrix. For the case of one-dimensional reduction, then the objective function is found to be y*. Taking the value of P as 1, through simplification and optimization of an objective function, the solution of the above formula is converted into the solution of the generalized eigenvalue of the following formula. In the following formula, λ is a feature value, and the dimensionality reduction result y is a feature vector corresponding to the minimum non-0 feature value, that is, Ly ═ λ Dy expands the dimensionality reduction process from one dimension to multiple dimensions to obtain a new objective function
Figure BDA0002859780330000052
Where P is a constant vector of dimension m, the dimensionality-reduced data y at this time*Taking m as 3, the invention obtains the final temperature value by taking m as 3
Figure BDA0002859780330000053
And step three is executed: the sensor temperature signal denoising processing is carried out through wavelet transform filtering, the wavelet base selection Coif5 carries out filtering processing on temperature measurement data low-frequency signals, the problem of distortion of traditional Fourier transform signals is greatly solved, an attenuation curve is smooth, noise is effectively removed, the characteristics of original signals are kept, and the effective signals are obtained by carrying out filtering processing on sensor data low-frequency oscillation signals through the process.
The measured temperatures are obtained five times in total, and after the laplace feature mapping processing, the temperature data are shown in table 1:
TABLE 1 measured temperature data processing Table
Number of measurements Measurement of temperature/. degree.C
For the first time 486.8
For the second time 459.7
The third time 519.3
Fourth time 501.9
Fifth time 479.5
Then, selecting wavelet basis Coif5 for filtering to perform sensor temperature signal denoising through wavelet transformation, obtaining a smoother and more accurate temperature attenuation signal curve diagram shown in 4(b) compared with the original temperature signal curve diagram 4(a), and obtaining an accurate result of the temperature measured by the instantaneous temperature sensor, and selecting a Coif5 wavelet basis to ensure the precision of the signal in the wavelet threshold denoising process; according to the specific characteristics of temperature data, the sparse characteristics of signals in wavelet domains under different wavelet bases are considered, the wavelet base with the best sparsity for input signals is selected, the denoising of wavelet threshold values is facilitated, the whole method is simple, convenient and quick, the rapid and accurate denoising of temperature signals is realized, the signal denoising effect and the signal processing efficiency in the application of a temperature measuring device are improved, and the accuracy of a measurement and control system of an engine test bed is further improved.

Claims (4)

1. A sensor error identification and elimination method based on a Laplace feature mapping algorithm is characterized by comprising the following steps:
the method comprises the following steps: arranging an engine combustion chamber outlet temperature field measuring device to be of an annular symmetrical structure, wherein the height of the measuring ring is coaxial with the engine, and the measuring ring is arranged far in front of the engine in the air inlet direction and is used for measuring the total air inlet pressure and the total air inlet temperature of the engine; in order to accurately obtain the total temperature value of the current position, a plurality of branch thermal resistance temperature sensors are used for measuring, and finally, the average value is obtained through multiple times of measurement; the temperature measuring device adopts an annular distribution measuring mode, and a plurality of sensors are dispersedly arranged on the same cross section in the mode, so that the measuring margin is increased, the measuring points are uniformly distributed, and the result is more accurate;
step two: creating a raw data set X ═ X for the measured temperature from step one1,x2,...,xN]∈RD×NWherein D is the data dimension, N is the number of samples, the number of near neighborhoods and the dimension reduction dimension D are set, and t belongs to RD×N(ii) a Finding out the neighborhood, creating neighborhood graph G, and searching each sample X by k-nearest neighbor methodiThe most recent k samples
Figure FDA0002859780320000011
The connection line of the two adjacent points is the edge in the neighborhood graph G; the calculation of G comprises two steps of neighbor selection and weight calculation; firstly, a field of data points is obtained by measuring a plurality of thermal resistance temperature sensors, then weights are defined for all edges, a weight matrix of high-dimensional space data is constructed, then the weight matrix is created to be a thermal kernel function, then characteristic decomposition is carried out, the dimension reduction process is expanded from one dimension to multiple dimensions, a target function of an LE algorithm is obtained, and then a target temperature value y after dimension reduction is obtained*；
Step three: and finally, performing noise reduction on the temperature signal of the sensor through wavelet transform filtering, and selecting a wavelet basis with the best noise reduction effect through experimental analysis of emphasis contrast wavelet bases Coif1, Coif2, Coif3, Coif4, Coif5 and other typical wavelet bases, so that the wavelet basis is selected to be Coif5 to perform filtering processing on the temperature measurement data low-frequency signal.
2. The method for sensor error identification and elimination based on Laplace eigenmap algorithm of claim, wherein the first step is:
the device for measuring the temperature field of the outlet of the combustion chamber of the engine is arranged to be of an annular symmetrical structure, the height of the measuring ring is coaxial with the engine, and the measuring ring is arranged far in front of the air inlet direction of the engine and used for measuring the total air inlet pressure and the total air inlet temperature of the engine; in order to accurately obtain the total temperature value of the current position, a plurality of branch thermal resistance temperature sensors are used for measuring, and finally, the average value is obtained through multiple times of measurement; the temperature measuring device adopts an annular distribution measuring mode, and a plurality of sensors are dispersedly arranged on the same cross section in the mode, so that the measuring margin is increased, the measuring points are uniformly distributed, and the result is more accurate.
3. The method for identifying and eliminating sensor errors based on the Laplace eigenmap algorithm as claimed in claim, wherein the second step is:
first, a raw data set X ═ X is created for the measured temperature1,x2,...,xN]∈RD×NWherein D is the data dimension, N is the number of samples, the number of near neighborhoods and the dimension reduction dimension D are set, and t belongs to RD×N(ii) a Finding out the neighborhood, creating neighborhood graph G, and searching each sample X by k-nearest neighbor methodiThe most recent k samples
Figure FDA0002859780320000012
The connection line of the two adjacent points is the edge in the neighborhood graph G; the calculation of G comprises two steps of neighbor selection and weight calculation; firstly, a field of data points is obtained by measuring by using a plurality of thermal resistance temperature sensors, then weights are defined for all edges, and a weight matrix of high-dimensional spatial data is constructed as follows:
Figure FDA0002859780320000021
then, a weight matrix is established to be a thermal kernel function, and then characteristic decomposition is carried out:
Lz＝λDz
wherein, the laplacian matrix L is D-W, D is the degree matrix, D is diag { D ═ D1,d2,d3,...,dN}，diIs a proximity matrix
Figure FDA0002859780320000022
For the case of one-dimensional reduction, the objective function of the LE algorithm is:
Figure FDA0002859780320000023
wherein (C)TIs a transpose of a matrix, WijHas a value of xiAnd xjThe greater the weight between, x is showniAnd xjThe more similar, if WijIs very large, according to the constraint of the above formula, yi-yjApproaching 0, i.e. and high-dimensional data point xiAnd xjCorresponding low dimensional data yiAnd yjThe method is also very similar, so that the local adjacency relation of the data before and after dimension reduction is kept, and P is a constant vector of m dimension; taking the value of P as 1, through simplifying and optimizing an objective function, the solution of the above formula is converted into the solution of the generalized eigenvalue of the following formula, wherein, lambda is the eigenvalue, and the dimensionality reduction result y is*That is, the feature vector corresponding to the minimum non-0 feature value, namely:
Ly＝λDy
the dimension reduction process is expanded from one dimension to multiple dimensions, and the objective function of the LE algorithm is expressed as follows:
y*＝argmintr(YLYT)
wherein tr () is the matrix tracing operation, the dimensionality reduction data y at this time*For m minimum eigenvectors corresponding to non-0 eigenvalues, the value of m is suggested to be [1,5 ]]Finally obtaining the final temperature value
Figure FDA0002859780320000024
In degrees celsius.
4. The method for identifying and eliminating sensor errors based on the Laplace eigenmap algorithm as claimed in claim, wherein the third step is:
because the temperature change rule of the tail flame of the engine is complex, the temperature measurement data inevitably has errors, the noise reduction processing of the temperature signal of the sensor is finally carried out through wavelet transform filtering, and the noise reduction effect is best when the wavelet basis is Coif5 through the experimental analysis of the important contrast wavelet basis Coif1, Coif2, Coif3, Coif4, Coif5 and other typical wavelet bases, therefore, the invention selects Coif5 to carry out filtering processing on the low-frequency signal of the temperature measurement data on the wavelet basis, thereby greatly overcoming the distortion problem of the traditional Fourier transform signal, producing smooth attenuation curve, effectively removing noise and keeping the characteristics of the original signal;
the basic idea of wavelet threshold denoising is to set a critical threshold, compare the wavelet coefficient with the critical threshold, if less than, the coefficient is mainly caused by noise, and eliminate the coefficient; if the coefficient is larger than the critical threshold value, the coefficient is mainly caused by signals, the part of the coefficient is left, and then the wavelet inverse transformation is carried out on the processed wavelet coefficient to obtain a denoised signal;
the wavelet denoising method comprises the following steps: wavelet transform is carried out on the signal f (t) with noise to obtain a group of wavelet decomposition coefficients Wj,kBy decomposing the wavelet coefficients Wj,kPerforming threshold processing to obtain estimated wavelet coefficient
Figure FDA0002859780320000025
Make it
Figure FDA0002859780320000026
Using estimated wavelet coefficients as small as possible
Figure FDA0002859780320000027
Performing wavelet reconstruction to obtain an estimated signal f (t), namely a denoised signal;
aiming at the difficulty of fast and accurate extraction of wavelet coefficients in wavelet denoising, a very simple method is provided for wavelet coefficients Wj,kCarrying out estimation; after wavelet decomposition is continuously carried out on f (t) for several times, a space distribution non-uniform signal C (k) is provided, and wavelet coefficients W on all scales are obtainedj,kWith larger values at certain specific locations, which correspond to odd locations and important information of the original signal C (k), and W at most other locationsj,kSmaller, for white noise, its corresponding wavelet coefficient Wj,kThe distribution is uniform at each scale and W increases with the scalej,kThe magnitude of the coefficient decreases; therefore, the general denoising method is to find a suitable number as a threshold value and apply a wavelet function W below the critical threshold valuej,kSet to zero and for wavelet functions W abovej,kThen it is retained or shrunk to obtain the estimated smallnessWave coefficient
Figure FDA0002859780320000031
It is understood to be essentially caused by the signal C (k), then for Wj,kReconstructing to reconstruct the original signal;
the invention processes the discrete time series X of noisy temperature data by LE algorithmn(t) continuous wavelet transform:
Figure FDA0002859780320000032
Figure FDA0002859780320000033
wherein, the theta number represents complex conjugate, s is resolution scale, t is time, n is time translation amount, delta t is time transformation amount, psi is mother wavelet psi0The non-dimensionalized result is calculated by the step to finally obtain the temperature signal data required by the invention, and a smooth data curve is formed.
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