CN113204879B - Improved Hankel matrix prediction model modeling method based on fluorescent oil film and application - Google Patents
Improved Hankel matrix prediction model modeling method based on fluorescent oil film and application Download PDFInfo
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Abstract
The invention discloses a modeling method and application of an improved Hankel matrix prediction model based on a fluorescent oil film, wherein the modeling method comprises the following steps: establishing a basic Hankel matrix prediction model; establishing an error correction prediction model according to the processing of the prediction value and the error value of the basic prediction model; and determining an improved Hankel matrix prediction model according to the prediction condition of the error correction prediction model. The modeling method can effectively solve the problems of tedious acquisition steps, time consumption and labor consumption of relation data of the gray scale of the fluorescent oil film image and the oil film thickness, more accurate data can be obtained through accurate prediction of extremely few acquired data, the complex operation of data acquisition is avoided, and a large amount of time and tool equipment are saved.
Description
Technical Field
The invention relates to the technical field of a modeling method for the thickness of a fluorescent oil film and the image gray value of the fluorescent oil film.
Background
The surface friction drag (surface friction drag for short) is one of the most important physical quantities in aerodynamics, is an important component of the total drag suffered by an aircraft during flight, can well describe the state of a turbulent boundary layer, and is one of the most difficult physical quantities to determine. The reduction of the friction resistance can not only reduce the oil consumption of the aircraft and improve the endurance time of the aircraft, but also mean that the surface heat flow of the supersonic aircraft is reduced, the weight of a heat-proof material is reduced, and the effective load is increased. The existing research shows that the surface friction of the novel civil aircraft during stable operation accounts for about half of the total resistance and far exceeds other resistance factors to occupy the leading position; the maximum surface friction of the supersonic aircraft developed in China can account for more than 50% of the total resistance, the running stability of the supersonic aircraft is seriously influenced, and the service life of the supersonic aircraft is directly related. Reducing surface friction is therefore of great importance to improve aircraft performance, reduce costs and save energy.
Most of the traditional methods for measuring the friction resistance have certain defects and limitations, such as a hot film method, a Preston tube method, a Stanton tube method, a friction balance method, a laser Doppler method and the like, wherein the hot film method is mainly used for measuring the heat on an electrically heatable metal film, and the friction resistance is obtained by resolving through establishing a mathematical model between the joule heat conversion rate and a fluid, but the method can cause distortion due to a temperature drift phenomenon; the Preston pipe and the Stanton pipe have high requirements on factors such as geometric appearance of a die, included angle of air flow and the like, and are difficult to flexibly apply; the friction balance method is characterized in that a floating element is arranged on a displacement sensor, the resultant force of surface friction resistance acting on the floating element can be directly measured, and the measurement precision is greatly influenced by environmental factors, traditional process manufacturing factors and human factors; the laser doppler measurement method uses the doppler effect generated by scattering of particles when they pass through a viscous underlayer having a streak light, but is difficult to apply to an unsteady measurement because of a low sampling rate due to a low trace particle density in the viscous underlayer.
In order to improve the traditional measurement method, the prior art provides a means for mixing silicone oil and fluorescent molecules according to a specific proportion to prepare a fluorescent oil film, according to a color reaction excited by the fluorescent oil film under ultraviolet irradiation, the thickness value of the oil film is represented by an oil film image gray value, and then friction distribution is calculated.
However, if the fluorescence oil film image gray value and oil film thickness value data are directly obtained through actual measurement, the fluorescence oil film image gray value and oil film thickness value data are generally complex and/or the collected data amount is small, for example, li Peng in 2012 provides a fluorescence oil film gray value and thickness data collection method, which is implemented by using a sampling device (the specific structure is shown in lieng "research on global surface friction stress direct measurement technology" nanjing aerospace university, 2012) built by a platform with a flat surface and placed by an optical glass slide with high light transmittance, and solving fluorescence oil films with continuous and different thickness values through a geometric relationship, wherein the sampling device satisfies the following requirements:
h and s are the thickness of the point to be measured and the length of the measuring area, H and F are the height of the glass slide and the length of the inclined plane collecting area of the glass slide respectively, and the thickness information of any point in the measuring area can be obtained through the device. However, the acquisition method has the disadvantages of more complicated steps, more mathematical conversion, time and labor consumption because each pixel point required to be acquired needs to be accurately positioned, and meanwhile, an acquisition system used by the acquisition method is very dependent on the smoothness and smoothness of the mold, so that the requirement on the mold is higher, and the scheme implementation cost is high.
Besides actual data acquisition, the research on the relation between the gray level of a fluorescent oil film image and the thickness of the fluorescent oil film image in the prior art is less, and a systematic model and a modeling method capable of obtaining the gray level and the thickness value are not provided.
In order to meet the data requirements, besides actual acquired data, other data besides the acquired data need to be used, in further processing, when interpolation is performed on the actually acquired data by a traditional interpolation method, the precision requirement can be met, and when interpolation is performed on other data besides the acquired data, especially under the condition that the interpolated data are far away from the acquired data, the precision of the data often cannot meet the requirement, and even error data can appear.
On the other hand, in 2014, mu and Chen establish a Hankel matrix for system identification, and the matrix is characterized in that a prediction model can be established through a very small amount of data, so that a large amount of data except for modeling data can be predicted, which is not possessed by a traditional interpolation method. However, the traditional Hankel matrix prediction model is low in precision, large in deviation when long data are predicted, and incapable of being directly applied to modeling of a fluorescence oil film image gray value and an oil film thickness value and obtaining an accurate prediction result.
Disclosure of Invention
The invention aims to provide a modeling method which can predict other available data through a small amount of data, has high prediction precision, can avoid a large number of data acquisition operations to a great extent, saves a large amount of time and tool equipment, and effectively solves the problems of complicated acquisition steps, time and labor consumption and small amount of available data of the fluorescent oil film image gray scale and oil film thickness data in the prior art. The invention also aims to provide specific application methods of the modeling method.
The invention firstly discloses the following technical scheme:
a modeling method of an improved Hankel matrix prediction model based on a fluorescent oil film comprises the following steps:
s1, establishing a basic Hankel matrix prediction model based on fluorescence oil film collected data;
s2, data prediction is carried out through the basic Hankel matrix prediction model;
s3, establishing an error correction prediction model of a basic Hankel matrix prediction model according to the processing of the predicted value obtained in the step S2 and the error value of the predicted value;
s4, data prediction is carried out through the error correction prediction model, and model prediction accuracy and/or prediction precision evaluation is carried out through prediction data;
and S5, if the prediction data obtained by the error correction prediction model is accurate and/or the prediction precision of the prediction data is improved, outputting the error correction prediction model as an improved Hankel matrix prediction model, and if the obtained prediction data is inaccurate and/or the prediction precision of the prediction data is not improved, taking the error correction prediction model as a basic Hankel matrix prediction model of S1 and continuously carrying out iterative updating according to the process from S2 to S5 until the improved Hankel matrix prediction model is obtained.
According to some preferred embodiments of the present invention, the processing of the predicted values and the error values comprises: and carrying out equalization processing on the error value, and correcting the predicted value through the error value after the equalization.
According to some preferred embodiments of the present invention, the step S3 comprises: and correcting the predicted value through the error value to obtain a corrected predicted value, and establishing the error correction prediction model through the corrected predicted value.
According to some preferred embodiments of the invention, the modeling method comprises:
(1) Establishing a basic Hankel matrix prediction model;
(2) Carrying out data prediction through the basic Hankel matrix prediction model;
(3) Averaging the error value generated by prediction;
(4) Correcting the prediction data according to the averaging processing result, replacing the original prediction data with the correction data, and establishing a first error correction prediction model of a basic Hankel matrix prediction model;
(5) Performing data prediction through a first error correction prediction model;
(6) And (3) if the data prediction is good, outputting the error correction prediction model as an improved Hankel matrix prediction model, and if the data prediction is wrong, taking the error correction prediction model as the basic Hankel matrix prediction model in the step (1) to continuously carry out iterative updating according to the processes of (2) to (6) until the improved Hankel matrix prediction model is obtained.
In some embodiments, whether the data prediction is good or not can be determined by whether the error correction prediction model is improved in prediction accuracy relative to the basic Hankel matrix prediction model, and if the prediction accuracy is improved, the data prediction is considered to be good.
According to some preferred embodiments of the invention, the first error-corrected prediction model is as follows:
Γw(n)＝[w(n)-wn]+Γwn (13)，
wherein w (n) represents an impulse response data set for model building, which can be specifically composed of a gray value of a pixel point in a fluorescent oil film image or a corresponding identifier thereof, such as a pixel point serial number and the like, and a corresponding oil film thickness value,
representing model prediction result data set, Δ ε(n)Express an errorDifference data set, G: (ε)(z-1) Denotes. DELTA.. Di(n)Z-domain transfer function of (Δ ε)nRepresenting error data set Δ ε(n)Wherein G represents a gray scale value at a certain time in the pulse data, Δ G represents a gray scale value difference between two adjacent elements in the pulse data, δ (G-n · Δ G) represents a pulse function, δ (G-k · Δ G) =1 holds when G = n · Δ G, n represents a system order size, and Γ ww =1nRepresenting the corrected pulse data set, wnDenotes w(n)Of (a) single modeling data, Γ w(n)Representing a new impulse response data set obtained by replacing its original impulse data set with the modified impulse data set.
According to some preferred embodiments of the invention, said step S3 comprises: and correcting the predicted value through the error value to obtain a corrected predicted value, adding the corrected predicted value into the set of predicted values to obtain an expanded predicted value, and establishing the error correction prediction model through the corrected predicted value.
According to some preferred embodiments of the invention, the modeling method comprises:
(1) Establishing the basic Hankel matrix prediction model;
(2) Performing data prediction through the basic Hankel matrix prediction model;
(3) Averaging the error value generated by prediction;
(4) Correcting the predicted data according to the averaging processing result, adding the corrected data into the original predicted data to obtain expanded data, and establishing a second error correction prediction model of the basic Hankel matrix prediction model according to the expanded data;
(5) Evaluating the accuracy of the second error correction prediction model;
(6) And (3) if the prediction precision is improved, outputting the error correction prediction model as an improved Hankel matrix prediction model, and if the prediction precision is not improved, taking the error correction prediction model as the basic Hankel matrix prediction model in the step (1) to continuously carry out iterative updating according to the processes from (2) to (6) until the improved Hankel matrix prediction model is obtained.
According to some preferred embodiments of the invention, the second error-corrected prediction model is as follows:
G(z-1)＝w1z-1+w2z-2+…wnz-n (17)
wherein, w(n)The impulse response data set used for model building is represented and can be specifically composed of gray values of pixel points in the fluorescent oil film image or corresponding marks thereof, such as pixel point serial numbers and the like, and corresponding oil film thickness values,
data set representing model prediction results, Δ ε(n)Indicating an error data set, G (z)-1) Represents Delta epsilon(n)Z-domain transfer function of (Δ ε)nRepresenting error data set Δ ε(n)G represents the gray scale at a certain time in the pulse dataThe value Δ G represents the difference between the gray values of two adjacent elements of the pulse data, δ (G-n.Δ G) represents the pulse function, δ (G-k.Δ G) when G = n.Δ G＝1N represents the system order size, Γ wnRepresenting the corrected pulse data set, wnDenotes w(n)Of (3) single modeling data, Γ w(n)Representing the expanded impulse response data set obtained from the r-th iteration,
representing the extended impulse response data set obtained in the (r + 1) th iteration,
represents passing through transfer function G (z)-1) The predicted data, r, represents the number of iterations,
the convergence condition is indicated.
According to some preferred embodiments of the present invention, the method for evaluating the prediction accuracy comprises: and subtracting the original data from the predicted data to obtain error data, taking the percentage value of the error data and the corresponding original data as an error rate, and representing the prediction precision by the size of the error rate.
The invention further provides some applications of the modeling method, such as obtaining more and accurate fluorescence oil film thickness data and image gray scale data thereof on the basis of a small amount of collected data through the modeling method.
The invention can be further applied to surface friction resistance analysis based on the thickness data of the fluorescent oil film and the image gray scale data thereof.
Compared with the traditional Hankel matrix prediction model which has no correction error function and can continuously accumulate and amplify generated errors, the errors are generated by the system and can also contain problems such as rounding calculation errors and the like, the method can greatly eliminate the error influence and realize the improvement of the model prediction precision by establishing the improved Hankel matrix prediction model, such as the first error correction prediction model or the matrix error correction prediction model in a specific implementation manner and the second error correction prediction model or the Hankel matrix high-order iteration error correction prediction model in a specific implementation manner.
The modeling method can effectively solve the problems of tedious acquisition steps, time consumption and labor consumption of relation data of the gray scale of the fluorescent oil film image and the oil film thickness, and can predict other data to be acquired through a small amount of data and keep high precision, so that the complicated operation of data acquisition is avoided to the great extent, and a large amount of time and tool equipment are saved.
Drawings
Fig. 1 is a collection device for data collection application in an embodiment.
Fig. 2 is a specific process for establishing the improved Hankel matrix prediction model in the present invention.
Fig. 3 is another specific process for establishing the improved Hankel matrix prediction model in the present invention.
Fig. 4 is a schematic flow chart of a specific data acquisition method according to an embodiment.
Fig. 5 is a schematic diagram of a specific working condition of data acquisition in embodiment 1.
Fig. 6 is a schematic diagram of pixel value equalization processing in embodiment 1.
Fig. 7 is a real captured picture obtained in example 1.
Detailed Description
The present invention is described in detail with reference to the following embodiments and drawings, but it should be understood that the embodiments and drawings are only for illustrative purposes and are not intended to limit the scope of the present invention. All reasonable variations and combinations that fall within the spirit of the invention are intended to be within the scope of the invention.
According to the technical scheme of the invention, some specific modeling methods of the improved Hankel matrix prediction model comprise the following steps:
s1, establishing a basic Hankel matrix prediction model;
s2, carrying out data prediction through the basic Hankel matrix prediction model;
s3, establishing an error correction prediction model of a basic Hankel matrix prediction model according to the processing of a predicted value and/or an error value generated by prediction;
s4, data prediction or prediction precision evaluation is carried out through the error correction prediction model;
and S5, if the prediction data obtained by the error correction prediction model is accurate and/or the prediction precision of the prediction data is improved, outputting the error correction prediction model as an improved Hankel matrix prediction model, and if the prediction data obtained by the error correction prediction model is inaccurate or the prediction precision of the error correction prediction model is not improved, taking the error correction prediction model as the basic Hankel matrix prediction model in the step (2) to continuously carry out iterative updating according to the process from S2 to S5 until the finally improved Hankel matrix prediction model is obtained.
The basic theory of the Hankel matrix prediction model is as follows:
let the Z-domain transfer function of the Hankel matrix prediction model be as shown in formula (2), wherein [ b1,b2…bn]Is the molecular coefficient, [ a ]1,a2…an]The number of the orders is determined by the numerator and the highest power of the denominator coefficient:
performing power series expansion on the formula (2) to obtain the following formula (3):
[ w ] in the formula (3)1,w2…wn]Substituting equation (3) into equation (2) to obtain equation (4) as the pulse coefficient which is the coefficient of the constant term obtained by expansion:
further developed and reduced to formula (5):
the product of equation (5) is transformed and simplified for the same power term, i.e.:
constructing impulse response data and transfer function molecular coefficient b by the equality of the coefficients corresponding to the same power level terms on both sides of the equal signnAnd denominator coefficient anIs expressed by equation (7):
the power series coefficients to the right of equation (7) are constructed in the form of a Hankel matrix:
the transfer function denominator coefficient anThe solution matrix of (2) is as shown in equation (9):
it can be seen that the molecular coefficient b of the transfer function can be obtained by constructing Hankel matrix for impulse response datanAnd denominator coefficient anAnd further obtaining a Z-domain transfer function prediction model.
According to the denominator coefficient a of the transfer function in the modelnHaving a direct correlation with impulse response data, bisecting the parent coefficient anBy optimisation, e.g. by direct action on denominator coefficients anThe impulse response data of (2) is corrected to obtain better resultsAnd (4) a good prediction effect.
Based on the above findings, the error-corrected prediction model may be further selected from:
A. the process of obtaining the improved Hankel matrix prediction model based on the first error correction prediction model is shown in fig. 2, and specifically includes:
(1) Establishing a basic Hankel matrix prediction model;
(2) Performing data prediction through the basic Hankel matrix prediction model;
(3) Averaging the error value generated by prediction;
(4) Correcting the predicted data according to the equalization processing result, replacing the original predicted data with the corrected data, and establishing a first error correction prediction model of a basic Hankel matrix prediction model;
(5) Carrying out data prediction through a first error correction prediction model;
(6) And (3) if the data prediction is good, outputting the error correction prediction model as an improved Hankel matrix prediction model, and if the data prediction is wrong, taking the error correction prediction model as the basic Hankel matrix prediction model in the step (2) and continuously performing iterative updating according to the processes from (2) to (6) until the final improved Hankel matrix prediction model is obtained.
And determining whether the data is well predicted or not by correcting the precision of the prediction model by the first error relative to the basic Hankel matrix prediction model, and if the precision is improved after correction, determining that the data is well predicted.
The first error correction prediction model may be further specifically constructed as follows:
let w (n) denote the impulse response data set used for model building,
representing the prediction result data set of the model pair w (n), an error data set represented by equation (10) is obtained:
wherein, delta epsilon(n)Indicating an error data set.
Establishing delta epsilon based on the basic theory of the Hankel matrix prediction model(n)Z domain transfer function G (ε)(z-1) And according to the Z-domain transfer function characteristic, expressing the Z-domain transfer function characteristic as a pulse model as follows:
in the formula (11) < delta > epsilonnRepresenting error data set Δ ε(n)In the data in (1), G represents a gray scale value at a certain time in the pulse data, Δ G represents a gray scale value difference between two adjacent elements in the pulse data, δ (G-n · Δ G) represents a pulse function, and δ (G-k · Δ G) =1 is true when G = n · Δ G.
Analysis of formulae (7), (8) and (9) with consideration of wnFor a single modeling data, and wnDirectly influencing the denominator coefficient anAfter the error correction processing, the following corrected pulse data group Γ w can be obtainedn：
The obtained correction pulse data Γ wnUpdating to the original number sequence to obtain a new data set Γ w (n) and establishing a data correction model as follows:
Γw(n)＝[w(n)-wn]+Γwn (13)。
and taking the corrected data group obtained by the data correction model as impulse response data group data of a Hankel matrix prediction model to obtain a corresponding Z-domain transfer function, namely obtaining a first error correction prediction model.
B. And a second error correction prediction model, namely a higher order iterative error correction prediction model.
In order to improve the accuracy of the prediction model, the invention also comprises a process of establishing a high-order system transfer function model in an iterative mode, namely expanding on the basis of the first error correction prediction model, for example, supplementing data predicted by the first error correction prediction model into an original pulse data column to expand the pulse data volume so as to establish a higher-order prediction model. In the process, the supplemented prediction data are data subjected to error correction, the accumulated effect of errors is reduced, the subsequent prediction result can step into the normal orbit, meanwhile, a Hankel matrix is constructed by the supplemented new pulse data, an improved prediction model is established, iterative calculation is carried out until the model precision is gradually improved to a convergence state, and finally prediction analysis is carried out.
The process of obtaining the improved Hankel matrix prediction model based on the model is shown in fig. 3, and specifically includes:
(1) Establishing a basic Hankel matrix prediction model;
(2) Performing data prediction through the basic Hankel matrix prediction model;
(3) Averaging the error value generated by prediction;
(4) Correcting the predicted data according to the averaging processing result, adding the corrected data into the original predicted data to obtain expanded data, and establishing a second error correction prediction model of the basic Hankel matrix prediction model according to the expanded data;
(5) And evaluating the precision of the second error correction prediction model, wherein the specific precision evaluation method can be as follows: subtracting the original data from the predicted data to obtain error data, dividing the error data by the corresponding original data, converting the error data into a percentage form, displaying the percentage form for convenient visual analysis, and finally analyzing the percentage error as a precision judgment standard;
(6) And (3) if the prediction precision is improved, outputting the error correction prediction model as an improved Hankel matrix prediction model, and if the prediction precision is not improved, taking the error correction prediction model as the basic Hankel matrix prediction model in the step (1) to continuously carry out iterative updating according to the processes from (2) to (6) until the final improved Hankel matrix prediction model is obtained.
The specific construction thereof can further comprise:
let w(n)For the impulse response data set of the model to be established, a Hankel matrix H (w) constructed by the impulse response data set is:
transfer function prediction model G (z) is established based on equation (14)-1)＝w1z-1+w2z-2+…wnz-n(17) And establishing an iterative formula, wherein
Representing a transfer function prediction model G (z)-1) Predicted data, r is the number of iterations. By combining the data correction models of equations (12) and (13) and adding the corrected data to the original impulse response data set, the following extended corrected impulse data set can be obtained
As shown in equation (15):
and taking the obtained expanded corrected pulse data set as pulse response data set of a Hankel matrix prediction model, obtaining a corresponding Z-domain transfer function, and iterating until an error data set obtained by the formula (10) meets the following convergence condition:
and obtaining a Z-domain transfer function in a final convergence state corresponding to the Z-domain transfer function, namely obtaining a second error correction prediction model.
The invention further provides specific data acquisition and correlation methods for image gray values and oil film thickness values of a fluorescent oil film which can be used for the model establishment, which can be realized by the existing acquisition device shown in the attached drawing 1, and comprises the following specific steps shown in the attached drawing 4:
calibrating photographic equipment such as a camera required by data acquisition to obtain internal and external parameters of the equipment, wherein the internal parameters comprise a camera focal length, a focal point coordinate and a radial distortion parameter, and the external parameters comprise a rotation matrix and a translation matrix, so that the conversion from a world coordinate system to a camera coordinate system is determined;
obtaining a fluorescent oil film and an ultraviolet light source, and carrying out ultraviolet color reaction on the oil film, for example, filling the oil film through a fluorescent oil film acquisition system, and starting the ultraviolet light source to carry out reaction;
acquiring a gray image of the oil film by using photographic equipment such as a camera;
judging whether the image effect is good, if not, performing oil film preparation and color reaction again, and if so, performing next gray value acquisition;
carrying out gray value acquisition on the gray image with good effect, comprising the following steps: resolving the pose, completing the conversion between the pixel coordinate and a world coordinate system, and acquiring a gray point set of the needed oil film;
and carrying out pixel proportion and geometric conversion on the collected gray points to obtain the oil film thickness corresponding to each point in the point set.
Example 1
The method for acquiring and correlating the data is used for acquiring and correlating the image gray value and the oil film thickness value of the fluorescent oil film.
The camera equipment uses a camera with the model of Canon EOS 550D, the horizontal resolution and the vertical resolution of the camera are 72dpi, the bit depth is 24, the camera equipment has the characteristics of high resolution, high acquisition speed, simplicity and convenience in operation and the like, the used ultraviolet light source is a machine vision ultraviolet lamp with the model of JZFZ-220/18-001, the effective power of the ultraviolet lamp is 18W +/-10%, and the camera equipment has the characteristic of uniform ultraviolet light emission.
In the test process, when the fluorescent oil film is in an excited state, in order to eliminate the interference of stray light such as an ultraviolet light source, ambient light and the like, a 520nm optical filter is additionally arranged at the lens of the camera so as to improve the precision of the pixel gray value.
In the apparatus shown in FIG. 1, the glass slide is an international standard glass slide, the length of the glass slide is 76.20mm, the width of the glass slide is 25.40mm, and the height of the glass slide is 0.95mm, and the specific collection steps performed by the apparatus are as follows:
placing a glass slide 2 on a flat smooth light-tight platform, wherein the platform can ensure the smoothness and the flatness thereof through high-precision machining and other modes;
pouring a proper amount of fluorescent oil film into a region which is not directly contacted with the glass slide 2 on the smooth platform, taking another glass slide 1 with the light transmittance of more than 95%, enabling one end of the glass slide 1 to be contacted with the smooth platform, and enabling the other end of the glass slide to be provided with the glass slide 2 to form an inclined plane, and enabling the fluorescent oil film below the glass slide 1 to be filled in a gap formed by the glass slide 1, the glass slide 2 and the smooth platform through the pressing of the glass slide 1;
turning on an ultraviolet lamp, acquiring a gray level image of an oil film through an acquisition working condition shown in fig. 5, under the acquisition working condition, establishing a spatial rectangular coordinate system by taking the end point of the left end of the glass slide as an origin, wherein the length of an effective acquisition region in the extension direction from the origin to the oil film is 70.00mm, namely the spatial coordinate of an initial acquisition point is (0, 0), the spatial coordinate of an end point is (7, 0), the unit is cm, and the height of an ultraviolet light source is 50cm, namely the spatial coordinate of the ultraviolet light source is (0, 50).
Under the above-mentioned collection procedure, the thickness of the oil film at different positions can be obtained as follows:
wherein H represents the thickness of the oil film point to be measured, s represents the length of the measuring area, and H and F represent the height of the glass slide and the length of the inclined plane collecting area of the glass slide 1 respectively.
In order to improve the stability of the gray value of the pixel, an average processing is performed on the pixel value to be measured, that is, a 3 × 3 square region is formed by collecting 8 pixel points around the pixel point to be measured and the measurement pixel point, and then the pixel values of 9 pixel points in the region are averaged to represent the size of the pixel value of the measurement pixel point, as shown in fig. 6. The number of the collected pixel points is 22, the shot and collected gray level images are analyzed by MATLAB software to establish a pixel value coordinate matrix, the space coordinate and the pixel coordinate of the initial collection point are respectively (0, 0), (610, 1020), and the space coordinate and the pixel coordinate of the final collection point are respectively (7, 0) and (2418, 1020). Since there is a decimal after the gray-scale value average processing, the gray-scale value is converted into an integer, and if the gray-scale value obtained by the gray-scale value average processing is 76.11 and the thickness is 78.09961, the corresponding thickness is converted into 77.98673 when the gray-scale value is converted into 76. After the thickness values of the 22 acquisition points are calculated by the formula (1), the pixel coordinates of the 22 acquisition points on a pixel coordinate system are solved and solved according to the pose, and MATLAB software is used for reading the pixel values of the pixel coordinates of the 22 acquisition points, so that the gray scale and thickness data of the fluorescent oil film comprising the data in the tables 1 and 2 can be obtained:
TABLE 1 fluorescent oil film Gray-thickness test data
TABLE 2 fluorescent oil film Gray-thickness test data (data for modeling)
| Serial number | 1* | 2* | 3* | 4* | 5* | 6* |
| Oil film ashValue Pixel | 100 | 96 | 92 | 88 | 84 | 80 |
| Oil film thickness value mum | 301.9912 | 235.6195 | 178.0973 | 142.1460 | 117.2566 | 96.23890 |
Through conversion, the Pixel scale coefficient lambda of the test is 38.71289 μm/Pixel, in the acquisition process, the brightness of the fluorescent oil film reaches the saturation state at about 320 μm, namely, the brightness does not increase, so the maximum acquired thickness is about 300 μm, the acquisition points are sequentially arranged from right to left, namely, the saturated gray value points are used, the shot real acquisition picture is shown in fig. 7, and the acquired data are obtained through arrangement and are shown in tables 1 and 2.
Example 2
Based on modeling data obtained in table 2 of embodiment 1, (serial number value, thickness value) is taken as w (n), and corresponding transfer functions are obtained through modeling processes of a traditional Hankel matrix model, a first error correction prediction model (Hankel matrix error correction model) and a second error correction prediction model (high-order iteration Hankel matrix error correction model) according to the specific implementation manner of the present invention, and are respectively shown as formulas (17), (18) and (19):
it can be seen that the prediction model established in the form of the Hankel matrix can well meet the special background that modeling is performed by using a small amount of data to predict other data and higher precision is kept.
Further, test data show that the prediction precision of the traditional Hankel model can reach 76.69%, the prediction precision of the improved algorithm Hankel array error correction model and the improved algorithm Hankel array high-order iteration error correction model based on the improved Hankel model are 85.69% and 89.25%, the precision of the improved algorithm Hankel array error correction model is respectively improved by 9% and 12.56% compared with that of the traditional Hankel array model, and the iteration of the high-order iteration error correction model reaches system convergence when the iteration reaches the fourth order. In the global friction resistance measurement, the thickness measurement of the fluorescent oil film is extremely important, and the thickness measurement reaches the micron level, so that the precision improvement of the improved algorithm has a great application value in the engineering practice.
The above examples are merely preferred embodiments of the present invention, and the scope of the present invention is not limited to the above examples. All technical schemes belonging to the idea of the invention belong to the protection scope of the invention. It should be noted that modifications and adaptations to those skilled in the art without departing from the principles of the present invention should also be considered as within the scope of the present invention.
Claims (6)
1. An improved Hankel matrix prediction model modeling method based on a fluorescent oil film is characterized by comprising the following steps: the method comprises the following steps:
s1, establishing a basic Hankel matrix prediction model based on fluorescence oil film collected data;
s2, carrying out data prediction through the basic Hankel matrix prediction model to obtain prediction data;
s3: correcting the prediction data through the error value to obtain corrected prediction data, and establishing a first error correction prediction model through the corrected prediction data, wherein the first error correction prediction model specifically comprises the following steps:
s31: averaging the error value generated by prediction to obtain an averaging result;
s32: correcting the prediction data according to the equalization processing result, replacing the original prediction data with the correction data, and establishing a first error correction prediction model of a basic Hankel matrix prediction model;
s4: performing data prediction through the first error correction prediction model;
s5: if the prediction data obtained through the first error correction prediction model is good, outputting the error correction prediction model as an improved Hankel matrix prediction model, and if the data prediction is wrong, taking the error correction prediction model as a basic Hankel matrix prediction model of S1 and continuously performing iterative updating according to the processes of S2-S5 until the improved Hankel matrix prediction model is obtained;
the fluorescence oil film acquisition data comprise pixel point gray values of fluorescence oil film images and corresponding oil film thickness values, and the prediction data are thicknesses of the fluorescence oil films.
2. The modeling method of claim 1, wherein: the first error-corrected prediction model is as follows:
Γw(n)＝[w(n)-wn]+Γwn (13)，
wherein, w(n)Representing the impulse response data set used for model building,
representing model prediction result data set, Δ ε(n)Representing error data set, G(ε)(z-1) Represents Delta epsilon(n)Z-domain transfer function ofnRepresenting error data set Δ ε(n)In the error data, G represents a gray scale value at a certain time in the pulse data, Δ G represents a gray scale value difference between two adjacent elements in the pulse data, δ (G-n · Δ G) represents a pulse function, δ (G-k · Δ G) =1 holds when G = n · Δ G, n represents a system order size, and Γ ww =1 holdsnRepresenting the corrected pulse data set, wnDenotes w(n)Of (3) single modeling data, Γ w(n)Representing a new impulse response data set obtained by replacing its original impulse data set with the modified impulse data set.
3. The modeling method of claim 1, wherein: the step S3 includes: and correcting the prediction data through the error value to obtain corrected prediction data, adding the corrected prediction data into a set of original prediction data to obtain expanded prediction data, and establishing the error correction prediction model through the expanded prediction data.
4. A modeling method in accordance with claim 3, wherein: the modeling method comprises the following steps:
(1) Establishing the basic Hankel matrix prediction model;
(2) Carrying out data prediction through the basic Hankel matrix prediction model;
(3) Averaging the error value generated by prediction;
(4) Correcting the predicted data according to the averaging processing result, adding the corrected data into the original predicted data to obtain expanded data, and establishing a second error correction prediction model of the basic Hankel matrix prediction model according to the expanded data;
(5) Evaluating the accuracy of the second error correction prediction model;
(6) And (3) if the prediction precision is improved, outputting the error correction prediction model as an improved Hankel matrix prediction model, and if the prediction precision is not improved, taking the error correction prediction model as the basic Hankel matrix prediction model in the step (1) to continuously carry out iterative updating according to the processes from (2) to (6) until the improved Hankel matrix prediction model is obtained.
5. The modeling method of claim 4, wherein: the second error-corrected prediction model is as follows:
G(z-1)＝w1z-1+w2z-2+…wnz-n (17)
wherein w(n)Representing the impulse response data set used for model building,
data set representing model prediction results, Δ ε(n)Indicating an error data set, G (z)-1) Denotes. DELTA.. Di(n)Z-domain transfer function ofnRepresenting error data set Δ ε(n)Wherein G represents a gray scale value at a certain time in the pulse data, Δ G represents a gray scale value difference between two adjacent elements in the pulse data, δ (G-n · Δ G) represents a pulse function, δ (G-k · Δ G) =1 holds when G = n · Δ G, n represents a system order size, and Γ ww =1nRepresenting the corrected pulse data set, wnDenotes w(n)Of (3) single modeling data, Γ w(n)Representing the expanded impulse response data set obtained from the r-th iteration,
representing the extended impulse response data set obtained in the (r + 1) th iteration,
represents the passage of a transfer function G (z)-1) The predicted data, r, represents the number of iterations,
the convergence condition is indicated.
6. A modeling method as claimed in claim 4 or 5, characterized in that: the method for evaluating the prediction precision comprises the following steps: and subtracting the original data from the predicted data to obtain error data, and representing the prediction precision by the error rate by taking the percentage value of the error data and the corresponding original data as the error rate.
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