CN103176951A - Method for balancing accuracy and calculated amount of multifunctional sensor signal reconstruction - Google Patents

Abstract

The invention discloses a method for balancing the accuracy and calculated amount of multifunctional sensor signal reconstruction, which relates to sensors. The method is used for balancing the accuracy and calculated amount of the existing multifunctional sensor signal reconstruction method based on B-spline and extend kalman filtering, and designed for achieving an effect that a balanced signal reconstruction method can ensure the accuracy, and the calculated amount is relatively low. The accuracy and calculated amount of the multifunctional sensor signal reconstruction are quantified by respectively using a minimum mean square error and the number of multiplication operation times; a fitness function is designed by using the two parameters; and the structure of a B-spline is optimized by using a genetic algorithm, so that the fitness function is minimum so as to realize the balancing on the accuracy and calculated amount of the signal reconstruction. According to the invention, the calculated amount required in the process of signal reconstruction can be greatly reduced on the basis of ensuring a high accuracy, and the method disclosed by the invention also can be applied to other multifunctional sensor signal reconstruction methods.

Description

Balance method for signal reconstruction precision and calculated amount of multifunctional sensor

Technical Field

The invention relates to a sensor, in particular to a method for balancing signal reconstruction accuracy and calculated amount of a multifunctional sensor.

Background

A multifunctional sensor is a sensor capable of measuring a plurality of physical quantities simultaneously, and is one of the main development trends of modern sensing technology. With the development of multifunctional sensors, the corresponding signal reconstruction method is also a problem which must be studied. At present, although there are a number of signal reconstruction methods suitable for multifunctional sensors, there are few methods that can ensure reconstruction accuracy and can be used on an intelligent chip, and a B-spline and kalman filter-based reconstruction method is one of them. However, in the current method, the structure of the B-spline model is generally selected manually without corresponding algorithm guidance, so that a large amount of unnecessary calculation is performed in order to achieve certain precision in the reconstruction process.

At present, a certain amount of research is carried out on a balance algorithm of a sensor at home and abroad, but some problems still exist. In most documents, a balance algorithm for reconstructing a sensor signal is not studied, and for the structure of a model, a method of multiple trials or depending on experience is generally adopted, as long as a required reconstruction effect is obtained, and other problems such as the calculation amount required by modeling, the complexity of the model and the like are not considered. In the literature (Wen, Liu Jian, Sun jin valuable, et al. research on the LS-SVM-based nonlinear multifunctional sensor signal reconstruction method, in the automated science and research report 2008,34(8): 869-. However, only the influence of the optimized parameters on the signal reconstruction error is studied in this document, and the influence on the calculation amount required for parameter identification is not studied. In the literature (Michele Gubian, Anna Marconato, Andrea Boni, et al. A study on incertation-Complex Transefs for dynamic Nonlinear Sensor Compensation. IEEE transactions on analysis and analysis, 2009,58 (1): 26-32) and literature (Michele Gubian, A. Marconato, A. Boni, et al. incertation-Complex Trans-offset for Sensor Compensation Den, AMUEM2007, Italy, 2007: 127-. In this paper, the authors have studied the methods of evaluating the accuracy and computational complexity during the calibration process and have achieved a balance between the two by optimizing the structure of the support vector machine. However, this document addresses the problem of single-function sensor compensation, and the object being optimized is the support vector machine.

Disclosure of Invention

The invention aims to provide a method for balancing signal reconstruction accuracy and calculated amount of a multifunctional sensor.

First, the B-spline algorithm is briefly described. The B-spline algorithm is an important tool for constructing complex nonlinear curves or surfaces. A curve or a curved surface constructed by the B-spline has good low-order smoothness, and the multifunctional sensor inverse model established by the curve or the curved surface can effectively avoid under-fitting and over-fitting phenomena, so that the signal reconstruction precision is improved. The basic structure of the B spline model is described by taking a three-input single-output model as an example. Given a set of sample data

And node sequences in three directions:

$\left\{\begin{array}{c}{\mathrm{tx}}_{-k+1}\&le;...\&le;{\mathrm{tx}}_0<{\mathrm{tx}}_1<...<{\mathrm{tx}}_L<{\mathrm{tx}}_{L+1}\&le;...\&le;{\mathrm{tx}}_{L+k}\\ {\mathrm{ty}}_{-k+1}\&le;...\&le;{\mathrm{ty}}_0<{\mathrm{ty}}_1<...<{\mathrm{ty}}_M<{\mathrm{ty}}_{M+1}\&le;...\&le;{\mathrm{ty}}_{M+k}\\ {\mathrm{tz}}_{-k+1}\&le;...\&le;{\mathrm{tz}}_0<{\mathrm{tz}}_1<...<{\mathrm{tz}}_N<{\mathrm{tz}}_{N+1}\&le;...\&le;{\mathrm{tz}}_{N+k}\end{array}\right.$

wherein,for inputting,

Is the output. Thus, a three-input single-output B-spline surface can be obtained:

$S(x_{\mathrm{\&alpha;}},y_{\mathrm{\&beta;}},z_{\mathrm{\&gamma;}})=\underset{u=-k+1}{\overset{L}{\mathrm{\&Sigma;}}}\underset{v=-k+1}{\overset{M}{\mathrm{\&Sigma;}}}\underset{w=-k+1}{\overset{N}{\mathrm{\&Sigma;}}}\left[h_{u,v,w}{B}_{u,\mathrm{tx}}^k\left(x_{\mathrm{\&alpha;}}\right)B_{v,\mathrm{ty}}^k\left(y_{\mathrm{\&beta;}}\right)B_{w,\mathrm{tz}}^k\left(z_{\mathrm{\&gamma;}}\right)\right]$

wherein, { h }_u,v,wThe control coefficient can be solved by extended Kalman filtering;

is a B sampleThe stripe basis function can be obtained by using a DeBoor-Cox, taking the x direction as an example:

$\left\{\begin{array}{c}{B}_{i,\mathrm{tx}}^1\left(x\right)=\left\{\begin{array}{c}1,{\mathrm{tx}}_i<x\&le;{\mathrm{tx}}_{i+1}\\ 0,\mathrm{others}\end{array}\right.\\ B_{i,\mathrm{tx}}^k\left(x\right)=\frac{{x-\mathrm{tx}}_i}{{\mathrm{tx}}_{i+k-1}-{\mathrm{tx}}_i}{B}_i^{k-1}\left(x\right)+\frac{{\mathrm{tx}}_{i+k}-x}{{\mathrm{tx}}_{i+k}-{\mathrm{tx}}_{i+1}}{B}_{i+1}^{k-1}\left(x\right)\end{array}\right.$

the balance algorithm provided by the invention comprises the following parts: quantizing the accuracy and the calculated amount of signal reconstruction; designing a fitness function by using the quantized parameters; and optimizing the structural parameters of the B spline model, namely the values of L, M and N by using a genetic algorithm with the aim of optimizing the fitness function.

The invention comprises the following steps:

1) determining the number of bits required for binary coding according to the value range of the node vector dimension in each input direction, and placing the node vector dimensions in all the input directions in the same binary number, wherein the binary number is an individual of a genetic algorithm;

2) randomly generating an initial population, namely an array consisting of a plurality of binary numbers;

3) let counter N =1, N representing the number of genetic algorithm cycles;

4) decoding all individuals in the population to obtain the corresponding node vector dimensions in all directions, and establishing a B spline model according to the node vector dimensions;

5) calculating the reconstruction minimum Mean Square Error (MSE) of each B spline model and the times of multiplication operations required by modeling;

6) calculating a fitness function of each individual;

7) according to the fitness function of each individual, carrying out selection, crossing and variation operations on the population to generate a new population;

8) judging whether the cycle number N reaches a preset value N_maxIf not, N = N +1 and jumps to step 3; if the set value is reached, the balance algorithm is ended, and an optimization result is given, namely the optimal individual (the individual with the minimum fitness function value) in the population at the moment.

Therefore, the optimal individual given by the balance algorithm is decoded, the node vector dimension of the obtained B-spline model in each input direction is the dimension optimized by the balance algorithm, and all the multifunctional sensors in the same batch are modeled by the B-spline model to realize signal reconstruction.

The invention respectively utilizes the minimum mean square error MSE (mean square error) and multiplication times to quantize the accuracy and the calculated amount of signal reconstruction, and the calculation formula of the MSE is as follows:

$\mathrm{MSE}=\sqrt{\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}(g_i-{\hat{g}}_i{)}^2}$

in the formula, n is the number of sample data;

g_ithe true value of the sample data;

after signal reconstruction, estimating the sample data;

the calculation formula of the times of multiplication is as follows:

Num＝Num_single×n

in the formula, Num is the number of times of multiplication operations required for reconstructing the whole signal;

Num_singleis the number of times of multiplication operations required by single Kalman filtering;

for a three-input single-output B-spline model, the times of multiplication operations required by single Kalman filtering are as follows:

Num_single＝λ³+2λ²+9λ+120

λ＝(L₁+k)(L₂+k)...(L_m+k)

where λ is the dimension of the Kalman filtering state vector;

m is the number of sensors being measured;

L₁,L₂…L_mvector dimension of the corresponding inner node for each measured quantity;

k is the order of the kalman filter.

The invention designs a fitness function by utilizing MSE and multiplication times:

Fitness＝Num_single+P＝λ³+2λ²+9λ+120+P

$P=\left\{\begin{array}{cc}0& \mathrm{MSE}<\mathrm{\&epsiv;}\\ a& \mathrm{MSE}\&GreaterEqual;\mathrm{\&epsiv;}\end{array}\right.$

wherein, Fitness is a Fitness function;

p is a penalty factor;

ε is the threshold value;

a is a penalty constant, which is typically set to a very large integer.

Optimizing the structural parameters of the B spline model by using a genetic algorithm to minimize a fitness function, wherein the genetic algorithm comprises the following steps:

1) b spline structural parameters, namely node vector dimensions in each input direction, namely L, M and N, are subjected to binary coding, and an initial population is given;

2) calculating a fitness function of individuals in the current population and MSE after signal reconstruction by using a B spline;

3) calculating the value of the fitness function;

4) selecting, crossing and mutating the existing population by using a genetic algorithm to generate a new population;

5) calculating the fitness function of the optimal individual in the new population, if the cycle number is higher than a preset value N_maxEnding, otherwise, returning to the step 2).

The method is used for the multifunctional sensor signal reconstruction method based on the B-spline and the extended Kalman filtering. The invention needs to optimize the model structure of the B-spline on a computer in advance, and then realizes the optimized model on an intelligent chip. On the basis of ensuring the reconstruction accuracy, the optimized model requires lower calculation amount for modeling than an unoptimized model.

The invention balances the precision and the calculated amount of the traditional multifunctional sensor signal reconstruction method based on B-spline and extended Kalman filtering, and aims to ensure that the balanced signal reconstruction method can ensure the precision and the calculated amount is relatively low. The precision and the calculated amount of the signal reconstruction method are quantized by respectively utilizing the minimum mean square error and the times of multiplication; a fitness function is designed by utilizing the two parameters; and optimizing the structure of the B spline by using a genetic algorithm to minimize a fitness function so as to balance the precision and the calculated amount of the signal reconstruction method. The invention can greatly reduce the calculation amount required in the signal reconstruction process on the basis of ensuring higher precision, and meanwhile, the balance thought of the invention can also be used for other multifunctional sensor signal reconstruction methods.

Drawings

FIG. 1 is a schematic diagram of a genetic algorithm based balancing method.

Fig. 2 is a flow chart of a multifunctional sensor signal reconstruction accuracy and calculation amount balancing method.

Detailed Description

The invention aims at a multifunctional sensor signal reconstruction method based on B-spline and extended Kalman filtering to realize the balance of reconstruction precision and calculated amount. The basic principle of the balance algorithm is shown in fig. 1, and the optimized object is the node vector dimension of a B-spline model in the reconstruction algorithm. For a multi-input B-spline model, each input corresponds to a node vector, and the balance algorithm optimizes the dimensionality of all the node vectors simultaneously. When all the node vector dimensions are determined, the B spline model is determined, so that the times of multiplication operations required by the model for reconstruction and the minimum Mean Square Error (MSE) which can be obtained according to the B spline model, and the value of the fitness function can be further calculated by using the two parameters. With the fitness function, the dimensionality of the node vector can be optimized by using a genetic algorithm, so that the value of the fitness function is reduced as much as possible. The reduction of the value of the fitness function means that a better minimum mean square error is obtained by using fewer times of multiplication operation, namely the balance of the fitness function and the minimum mean square error is achieved. When the fitness function is minimum, the corresponding structural parameters of the B-spline model, namely the node vector dimension in each input direction, are the required optimization parameters of the B-spline model, and the method can be used for signal reconstruction of the multifunctional sensor.

A specific balancing method flowchart is shown in fig. 2.

1) Determining the number of bits required for binary coding according to the value range of the node vector dimension in each input direction, and placing the node vector dimensions in all the input directions in the same binary number, wherein the binary number is an individual of a genetic algorithm;

2) randomly generating an initial population, namely an array consisting of a plurality of binary numbers;

3) let counter N =1, N representing the number of genetic algorithm cycles;

4) decoding all individuals in the population to obtain the corresponding node vector dimensions in all directions, and establishing a B spline model according to the node vector dimensions;

5) calculating the reconstruction minimum Mean Square Error (MSE) of each B spline model and the times of multiplication operations required by modeling;

6) calculating a fitness function of each individual;

7) according to the fitness function of each individual, carrying out selection, crossing and variation operations on the population to generate a new population;

8) judging whether the cycle number N reaches a preset value N_maxIf not, N = N +1 and jumps to step 3; if the set value is reached, the balance algorithm is ended, and an optimization result is given, namely the optimal individual (the individual with the minimum fitness function value) in the population at the moment.

Therefore, the optimal individual given by the balance algorithm is decoded, the node vector dimension of the obtained B-spline model in each input direction is the dimension optimized by the balance algorithm, and all the multifunctional sensors in the same batch are modeled by the B-spline model to realize signal reconstruction.

Claims (4)

1. A balance method for signal reconstruction precision and calculated quantity of a multifunctional sensor is characterized by comprising the following steps:

1) determining the number of bits required for binary coding according to the value range of the node vector dimension in each input direction, and placing the node vector dimensions in all the input directions in the same binary number, wherein the binary number is an individual of a genetic algorithm;

2) randomly generating an initial population, namely an array consisting of a plurality of binary numbers;

3) let counter N =1, N representing the number of genetic algorithm cycles;

4) decoding all individuals in the population to obtain the corresponding node vector dimensions in all directions, and establishing a B spline model according to the node vector dimensions;

5) calculating the reconstruction minimum Mean Square Error (MSE) of each B spline model and the times of multiplication operation required by modeling;

6) calculating a fitness function of each individual;

7) according to the fitness function of each individual, carrying out selection, crossing and variation operations on the population to generate a new population;

8) judging whether the cycle number N reaches a preset value N_maxIf not, N = N +1 and jumps to step 3; and if the set value is reached, ending the balance algorithm, and giving an optimization result, namely the optimal individual in the population at the moment.

2. The method for balancing reconstruction accuracy and computation workload of a multifunctional sensor signal as claimed in claim 1, wherein in step 5), the computation formula of the reconstructed minimum mean square error MSE is:

$\mathrm{MSE}=\sqrt{\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{(g_i-{\hat{g}}_i)}^2}$

in the formula, n is the number of sample data;

g_ithe true value of the sample data;

after signal reconstruction, estimating the sample data;

the calculation formula of the times of multiplication is as follows:

Num＝Num_single×n

in the formula, Num is the number of times of multiplication operations required for reconstructing the whole signal;

Num_singleis the number of times of multiplication operations required by single Kalman filtering;

for a three-input single-output B-spline model, the times of multiplication operations required by single Kalman filtering are as follows:

Num_single＝λ³+2λ²+9λ+120

λ＝(L₁+k)(L₂+k)...(L_m+k)

where λ is the dimension of the Kalman filtering state vector;

m is the number of sensors being measured;

L₁,L₂…L_mvector dimension of the corresponding inner node for each measured quantity;

k is the order of the kalman filter.

3. The method for balancing the reconstruction accuracy and the calculation amount of the multifunctional sensor signal according to claim 1, wherein in the step 6), the formula for calculating the fitness function of each individual is as follows:

Fitness＝Num_single+P＝λ³+2λ²+9λ+120+P

$P=\left\{\begin{array}{cc}0& \mathrm{MSE}<\mathrm{\&epsiv;}\\ a& \mathrm{MSE}\&GreaterEqual;\mathrm{\&epsiv;}\end{array}\right.$

wherein, Fitness is a Fitness function;

p is a penalty factor;

ε is the threshold value;

a is a penalty constant, which is typically set to a very large integer.

4. The method for balancing reconstruction accuracy and computational complexity of a multi-function sensor signal as claimed in claim 1, wherein the structural parameters of the B-spline model are optimized using a genetic algorithm to minimize the fitness function, the genetic algorithm comprising the steps of:

1) b spline structural parameters, namely node vector dimensions in each input direction, namely L, M and N, are subjected to binary coding, and an initial population is given;

2) calculating a fitness function of individuals in the current population and MSE after signal reconstruction by using a B spline;

3) calculating the value of the fitness function;

4) selecting, crossing and mutating the existing population by using a genetic algorithm to generate a new population;

5) calculating the fitness function of the optimal individual in the new population, if the cycle number is higher than a preset value N_maxEnding, otherwise, returning to the step 2).

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