Journal of Spectroscopy

Volume 2016 (2016), Article ID 5616503, 12 pages

http://dx.doi.org/10.1155/2016/5616503

## Spectral Quantitative Analysis Model with Combining Wavelength Selection and Topology Structure Optimization

^{1}School of Automation and Information Engineering, Xi’an University of Technology, Xi’an, Shaanxi 710048, China^{2}Shaanxi Key Laboratory of Smart Grid and State Key Laboratory of Electrical Insulation and Power Equipment, School of Electrical Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China

Received 12 June 2016; Accepted 15 September 2016

Academic Editor: K. S. V. Krishna Rao

Copyright © 2016 Qian Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Spectroscopy is an efficient and widely used quantitative analysis method. In this paper, a spectral quantitative analysis model with combining wavelength selection and topology structure optimization is proposed. For the proposed method, backpropagation neural network is adopted for building the component prediction model, and the simultaneousness optimization of the wavelength selection and the topology structure of neural network is realized by nonlinear adaptive evolutionary programming (NAEP). The hybrid chromosome in binary scheme of NAEP has three parts. The first part represents the topology structure of neural network, the second part represents the selection of wavelengths in the spectral data, and the third part represents the parameters of mutation of NAEP. Two real flue gas datasets are used in the experiments. In order to present the effectiveness of the methods, the partial least squares with full spectrum, the partial least squares combined with genetic algorithm, the uninformative variable elimination method, the backpropagation neural network with full spectrum, the backpropagation neural network combined with genetic algorithm, and the proposed method are performed for building the component prediction model. Experimental results verify that the proposed method has the ability to predict more accurately and robustly as a practical spectral analysis tool.

#### 1. Introduction

Spectral quantitative analysis is a nondestructive and fast measurement technique and has been used in a variety of chemical fields [1–3]. The method measures the chemical composition dependent absorption of light that occurs at different wavelengths [4]. Based on the obtained wavelength signals, the spectral quantitative analysis model is built to predict the component concentrations by the regression algorithms [5].

Partial least squares (PLS) is a classical multivariate regression approach for spectroscopy quantitative analysis, and it could handle the multiple correlation among the input wavelength signals [6]. Nevertheless, PLS is a linear regression algorithm essentially [7], and the nonlinearity of wavelength signals may be generated by the instrument variation and the analyte characteristics [8]. To deal with the nonlinear factors, neural network is always adopted for spectral model. Neural network could approximate any function by some simple interconnected processing units whose structure is inspired by animal brains [9, 10]. Backpropagation neural network (BPNN), as a popular neural network, uses the mean square error and the gradient descent for modifying the connection weights of the neurons [11]. The topology structure of BPNN is usually determined by the human experience [12] and may affect the model effectiveness. That may be one reason why three-layer BPNN is widely used [13–16].

Moreover, the spectral instrument usually records a large number of spectral wavelength signals and the regression model is generally performed based on the obtained wavelengths. However, not all of the obtained wavelengths have the useful information, and the wavelengths without any critical information would corrupt the prediction model [17, 18]. Therefore, wavelengths selection is a vital process for spectral quantitative analysis, and the goal of wavelengths selection is to determine a subset of the obtained spectral wavelengths that could generate the smallest possible errors of the regression models [19, 20]. Some statistical techniques have been adopted for the wavelength selection, and the importance of each wavelength could be estimated according to the statistical features of the prediction model [21, 22]. Uninformative variable elimination (UVE) is proposed to eliminate the wavelengths that do not contain much information for analyte prediction than random variables [23]. Although UVE is better than the statistical wavelength selection method [24, 25], the effectiveness of UVE would be affected by the quality of the random variables and the selection result is scattered throughout the spectrum [26].

BPNN could be optimized by the heuristic algorithm, and BPNN based on genetic algorithm (GA-BPNN) is proposed for determining the initial connection weights and the thresholds in a fixed topology structure [27, 28]. Furthermore, the wavelength selection could seem as a combinatorial problem; the genetic algorithm combined with PLS (GA-PLS) is presented, where GA finds the optimal subset of wavelengths associated with the PLS model [29, 30]. Because the model structure should be determined based on the number of the selected wavelengths, wavelength selection and the topology structure of BPNN would be optimized simultaneously, that is, a hybrid optimization problem. Evolutionary programming (EP) having no fixed structure outperforms with GA and is suitable for the hybrid optimization problem [31, 32]. Like GA, EP has the crossover operation and the mutation operation. However, the crossover operation of EP is limited by the chromosome form for the hybrid optimization problem, that may result in the side-effect, and EP without the crossover process would not reduce the search efficiency [33]. Furthermore, EP generally has the static mutation probability, and EP may fall into the local minima, which is similar to other searching algorithms [34].

In this paper, a spectral quantitative analysis model with combining wavelength selection and topology structure optimization is proposed. For the proposed method, BPNN is adopted for building the component prediction model, and the simultaneousness optimization of the wavelength selection and the topology structure of BPNN is realized by the nonlinear adaptive evolutionary programming (NAEP). The hybrid chromosome in binary scheme of NAEP has four fragments, which represent the number of the hidden layers of BPNN, the number of neurons in each hidden layer, the selection of spectral wavelengths, and two adaptive parameters of the mutation probability of NAEP, respectively. Hence, a chromosome represents an optimization plan. NAEP only has the mutation operation for the next generation, and the mutation probability of each chromosome is updated by a nonlinear equation with considering two adaptive parameters and the fitness values. For the initial generation of NAEP, each chromosome is encoded randomly. BPNN is performed on the calibration set based on different optimization plans represented by different chromosomes. The root-mean-squares error of cross-validation (RMSECV) is the fitness function; namely, the lower the RMSECV, the better the chromosome. The better parent chromosomes would be put into the next generation. The mutation probabilities of other chromosomes are updated according to the latest evaluation results, and the chromosomes are evolved only by the mutation operation. The evolution process of NAEP terminates based on the stop condition. The chromosome with lowest fitness value is the final result; namely, the selected wavelength and the corresponding topology structure of BPNN are determined. Two real flue gas datasets are employed in the experiments. The effectiveness of PLS, BPNN, GA-BPNN, UVE, GA-PLS, and the proposed method is compared.

The remainder of this paper is organized as follows. In Section 2, The related methods are demonstrated. In Section 3, the proposed method is presented. In Section 4, the experimental results are discussed. Section 5 concludes the paper.

#### 2. The Related Methods

##### 2.1. PLS

For PLS, represents the input wavelength signals, and the component can be expressed bywhere is the matrix of regression coefficients and is the error vector.

It assumes that a small number of the latent variables are refined by linear combinations of the vectors of . Then (1) can be transformed to where the matrix is corresponding to the latent variables and is the regression coefficients vector.

For , is the input matrix, is the matrix of weight loading representing the correlation between and , and is the matrix indicating the influence of .

##### 2.2. BPNN

BPNN connects the input layer and the output layer by one or more hidden layers. For spectroscopy quantitative analysis, the wavelengths are the signals of the input layer and the component concentration is the signal of the output layer [35]. A neuron is an activation function which is described by the tansig function, and the transfer function of the output layer is a purelin function [36]. The training process BPNN has the information forward-propagation algorithm and the error backpropagation training algorithm [11]. For the information forward-propagation algorithm, the values of each layer are calculated based on the activation function and the values of the previous layer. For the error backpropagation training algorithm, the error is propagated from the output layer to the input layer, and the weights are regulated by feedback. The modification of the weights and the offset values makes the actual output be closer to the expected output.

##### 2.3. GA-BPNN

For GA-BPNN, the chromosome is encoded for the initial connection weights and the thresholds of a fixed topology structure. The individuals of the father generation are generated randomly. Then, BPNN is performed based on the information represented by each individual, and the fitness value of each individual is evaluated. Some individuals are reserved for the next generation during the selection operation and their fitness values have a great impact on the reserve probability. Some new individuals are obtained by the crossover operation and the mutation operation. The reserved individuals and the new individuals form the next generation, and the iteration procedure is running constantly until the program satisfies its requirements. After the initial weights are determined, the backpropagation training method is used to adjust the final weights of BPNN.

##### 2.4. UVE

For UVE, an auxiliary matrix containing random noise is generated firstly and it has the same size as the input matrix. Then, the input matrix is combined with the auxiliary matrix to form the combination matrix, which has twice as many wavelength signals as the input matrix. PLS is performed on the combination matrix with the leave-one-out procedure. The criterion value of each column of the combination matrix is estimated by the average of its regression vector and its standard deviation. The original wavelength signal whose criterion value is not larger than a threshold is the uninformative wavelength and would be eliminated, where the threshold is set as the maximum value of the ratio of coefficient to the standard deviation of the auxiliary matrix region. Hence, UVE selects the wavelengths swiftly and practically.

##### 2.5. GA-PLS

In the GA-PLS method, the chromosome is coded by a binary string, and the length of a chromosome is equal to the number of all the wavelengths. Each gene of the chromosome is 1 or 0, which indicates that the wavelength is selected or dropped. For GA-PLS, a random population including a number of chromosomes is initialized, and the PLS model is built for each chromosome, where each chromosome represents a solution of wavelength selection. The prediction precision of PLS model is adopted as the fitness values. A new population is generated by the selection, the crossover, and the mutation. The iteration process is repeated and terminates with reaching the condition, which is the number of iterations or a predefined fitness value. Then, the chromosome with the smallest fitness value is the final result of the wavelength selection.

#### 3. The Proposed Method

For the proposed method, BPNN is adopted for building the component prediction model, and NAEP simultaneously optimizes the wavelength selection and the topology structure of BPNN.

For the new individuals of the next generation, NAEP has not the crossover operation and only has the mutation operation in evolving process. The mutation probability () is updated by where and are two adaptive parameters and is the normalized fitness value.

The hybrid chromosome in binary scheme of NAEP has four fragments, which is shown in Figure 1. Fragment 1 represents the number of the hidden layers (). With considering the model complexity of BPNN, fragment 1 has three genes; namely, the maximum value of is 7. Fragment 2 has twenty-eight genes and every four genes are used for representing the number of neurons in the hidden layer; namely, the maximum value of neurons in each hidden layer is 15. If is the number of hidden layers determined by fragment 1, the values of the genes from the position to the end position of fragment 2 are all zero. Fragment 3 is used for the wavelength selection. The length of fragment 3 is equal to the number of all the wavelengths. Each gene of fragment 3 is 1 or 0, which represents that the corresponding wavelength is selected or dropped. Fragment 4 adopts two parts for representing and , respectively, and each part has two genes. The binary value of part 1 is 00, 01, 10, or 11, which represents that is 0.05, 0.1, 0.15, or 0.2, respectively. In the same way, the different binary values of part 2 represent that is 0.35, 0.45, 0.55, or 0.65.