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In this article, a simple system will be presented to measure reflectance of metallic surfaces quickly and precisely based on goniospectrophotometric geometry. The paper aims to discuss these issues.

This system works by capturing reflected light from different colored patches by digital camera and with the knowledge of spectral power distribution of light source and defined observer, reflection of each sample can be reproduced. By fixing the light source, the position of the detector would be eliminated to four angles of observation.

This method can achieve acceptable reconstruction accuracy for metallic samples. This approach confirmed repeatability and practicality of the simple imaging acquisition to replace spectral reflectance measurement devices in different viewing angles.

The reflectance of metallic samples has been measured at several angles such as 20°, 45°, 75° and 110° from specular reflection. A simple system was used to measure multi-angle reflectance of metallic surfaces by digital camera. By suggested system can be measured the reflectance without contact and limitation in the shape of surfaces. This method achieved acceptable reconstruction accuracy for metallic samples. This simple imaging acquisition is comparable with goniospectrophotometer for measuring multi-angle reflectance of metallic samples.

The Hurst exponent has been very important in telling the difference between fractal signals and explaining their significance. For estimators of the Hurst exponent, accuracy and efficiency are two inevitable considerations. The main purpose of this study is to raise the execution efficiency of the existing estimators, especially the fast maximum likelihood estimator (MLE), which has optimal accuracy.

A two-stage procedure combining a quicker method and a more accurate one to estimate the Hurst exponent from a large to small range will be developed. For the best possible accuracy, the data-induction method is currently ideal for the first-stage estimator and the fast MLE is the best candidate for the second-stage estimator.

For signals modeled as discrete-time fractional Gaussian noise, the proposed two-stage estimator can save up to 41.18 per cent the computational time of the fast MLE while remaining almost as accurate as the fast MLE, and even for signals modeled as discrete-time fractional Brownian motion, it can also save about 35.29 per cent except for smaller data sizes.

The proposed two-stage estimation procedure is a novel idea. It can be expected that other fields of parameter estimation can apply the concept of the two-stage estimation procedure to raise computational performance while remaining almost as accurate as the more accurate of two estimators.

In order to overcome the uncertainty and improve the accuracy of spectral estimation, this paper aims to establish a grey fuzzy prediction model of soil organic matter content by using grey theory and fuzzy theory.

Based on the data of 121 soil samples from Zhangqiu district and Jiyang district of Jinan City, Shandong Province, firstly, the soil spectral data are transformed by spectral transformation methods, and the spectral estimation factors are selected according to the principle of maximum correlation. Then, the generalized greyness of interval grey number is used to modify the estimation factors of modeling samples and test samples to improve the correlation. Finally, the hyper-spectral prediction model of soil organic matter is established by using the fuzzy recognition theory, and the model is optimized by adjusting the fuzzy classification number, and the estimation accuracy of the model is evaluated using the mean relative error and the determination coefficient.

The results show that the generalized greyness of interval grey number can effectively improve the correlation between soil organic matter content and estimation factors, and the accuracy of the proposed model and test samples are significantly improved, where the determination coefficient R² = 0.9213 and the mean relative error (MRE) = 6.3630% of 20 test samples. The research shows that the grey fuzzy prediction model proposed in this paper is feasible and effective, and provides a new way for hyper-spectral estimation of soil organic matter content.

The research shows that the grey fuzzy prediction model proposed in this paper can not only effectively deal with the three types of uncertainties in spectral estimation, but also realize the correction of estimation factors, which is helpful to improve the accuracy of modeling estimation. The research result enriches the theory and method of soil spectral estimation, and it also provides a new idea to deal with the three kinds of uncertainty in the prediction problem by using the three kinds of uncertainty theory.

The paper succeeds in realizing both the grey fuzzy prediction model for hyper-spectral estimating soil organic matter content and effectively dealing with the randomness, fuzziness and grey uncertainty in spectral estimation.

In order to improve the estimation accuracy of soil organic matter, this paper aims to establish a modified model for hyperspectral estimation of soil organic matter content based on the positive and inverse grey relational degrees.

Based on 82 soil sample data collected in Daiyue District, Tai'an City, Shandong Province, firstly, the spectral data of soil samples are transformed by the first order differential and logarithmic reciprocal first order differential and so on, the correlation coefficients between the transformed spectral data and soil organic matter content are calculated, and the estimation factors are selected according to the principle of maximum correlation. Secondly, the positive and inverse grey relational degree model is used to identify the samples to be identified, and the initial estimated values of the organic matter content are obtained. Finally, based on the difference information between the samples to be identified and their corresponding known patterns, a modified model for the initial estimation of soil organic matter content is established, and the estimation accuracy of the model is evaluated using the mean relative error and the determination coefficient.

The results show that the methods of logarithmic reciprocal first order differential and the first-order differential of the square root for transforming the original spectral data are more effective, which could significantly improve the correlation between soil organic matter content and spectral data. The modified model for hyperspectral estimation of soil organic matter has high estimation accuracy, the average relative error (MRE) of 11 test samples is 4.091%, and the determination coefficient (R²) is 0.936. The estimation precision is higher than that of linear regression model, BP neural network and support vector machine model. The application examples show that the modified model for hyperspectral estimation of soil organic matter content based on positive and inverse grey relational degree proposed in this article is feasible and effective.

The model in this paper has clear mathematical and physics meaning, simple calculation and easy programming. The model not only fully excavates and utilizes the internal information of known pattern samples with “insufficient and incomplete information”, but also effectively overcomes the randomness and grey uncertainty in the spectral estimation of soil organic matter. The research results not only enrich the grey system theory and methods, but also provide a new approach for hyperspectral estimation of soil properties such as soil organic matter content, water content and so on.

The paper succeeds in realizing both a modified model for hyperspectral estimation of soil organic matter based on the positive and inverse grey relational degrees and effectively dealing with the randomness and grey uncertainty in spectral estimation.

This study aims to improve the accuracy of hyperspectral estimation of soil organic matter content.

Based on the uncertainty in spectral estimation, 76 soil samples collected in Zhangqiu District, Jinan City, Shandong Province, were studied in this paper. First, the spectral transformation of the spectral data after denoising was carried out by means of 11 transformation methods such as reciprocal and square, and the estimation factor was selected according to the principle of maximum correlation. Secondly, the grey weighted distance was used to calculate the grey relational degree between the samples to be estimated and the known patterns, and the local linear regression estimation model of soil organic matter content was established by using the pattern samples closest to the samples to be identified. Thirdly, the models were optimized by gradually increasing the number of modeling samples and adjusting the decision coefficient, and a comprehensive index was constructed to determine the optimal predicted value. Finally, the determination coefficient and average relative error are used to evaluate the validity of the model.

The results show that the maximum correlation coefficient of the seven estimated factors selected is 0.82; the estimation results of 14 test samples are of high accuracy, among which the determination coefficient R² = 0.924, and the average relative error is 6.608%.

Studies have shown that it is feasible and effective to estimate the content of soil organic matter by using grey correlation local linear regression model.

The paper succeeds in realizing both the soil organic matter hyperspectral grey relation estimating pattern based on the grey relational theory and the estimating pattern by using the local linear regression.

To develop a new method for estimation of damage configuration in composite laminate structure using acoustic wave propagation signal and a reduction‐prediction neural network to deal with high dimensional spectral data.

A reduction‐prediction network, which is a combination of an independent component analysis (ICA) and a multi‐layer perceptron (MLP) neural network, is proposed to quantify the damage state related to transverse matrix cracking in composite laminates using acoustic wave propagation model. Given the Fourier spectral response of the damaged structure under frequency band‐selective excitation, the problem is posed as a parameter estimation problem. The parameters are the stiffness degradation factors, location and approximate size of the stiffness‐degraded zone. A micro‐mechanics model based on damage evolution criteria is incorporated in a spectral finite element model (SFEM) for beam type structure to study the effect of transverse matrix crack density on the acoustic wave response. Spectral data generated by using this model is used in training and testing the network. The ICA network called as the reduction network, reduces the dimensionality of the broad‐band spectral data for training and testing and sends its output as input to the MLP network. The MLP network, in turn, predicts the damage parameters.

Numerical demonstration shows that the developed network can efficiently handle high dimensional spectral data and estimate the damage state, damage location and size accurately.

Only numerical validation based on a damage model is reported in absence of experimental data. Uncertainties during actual online health monitoring may produce errors in the network output. Fault‐tolerance issues are not attempted. The method needs to be tested using measured spectral data using multiple sensors and wide variety of damages.

The developed network and estimation methodology can be employed in practical structural monitoring system, such as for monitoring critical composite structure components in aircrafts, spacecrafts and marine vehicles.

A new method is reported in the paper, which employs the previous works of the authors on SFEM and neural network. The paper addresses the important problem of high data dimensionality, which is of significant importance from practical engineering application viewpoint.

The purpose of this paper is to establish the grey relational estimating model of soil pH value based on hyper-spectral data.

As to the uncertainty of the factors affecting the soil pH value estimation based on hyper-spectral, the grey weighted relation estimation model was set up according to the grey system theory. Then the linear regression correction model is established according to the difference and grey relation degree information between the estimated samples and their corresponding pattern. At the same time, the model was applied to Hengshan county of Shanxi province.

The results are convincing: not only that the linear regression correction model of grey relation estimating pattern of soil pH value based on hyper-spectral data is valid, but also the model’s estimating accuracy is higher, which the corrected average relative error is 0.2578 per cent, and the decision coefficient R²=0.9876.

The method proposed in the paper can be used at soil pH value hyper-spectral inversion and even for other similar forecast problem.

The paper succeeds in realising both the soil pH value hyper-spectral grey relation estimating pattern based on the grey relational theory and the correction model of the estimating pattern by using the linear regression.

This paper attempts to establish the grey GM(0,N) estimation model of the soil organic matter content spectral inversion under the uncertainties between soil organic matter contents and spectral characteristics and the theory of grey system.

At first, based on the uncertainty of the relationship between the soil organic matter content and spectral characteristics, using the ordered grey accumulation generation and grey GM(0, N) model to establish hyper‐spectral grey estimation model of soil organic matter content. Second, the presented model is used to estimate soil organic matter of Hengshan County in Shanxi province in the last part of the paper.

The results are convincing: not only that soil organic matter content spectral inversion grey GM(0, N) model based on the ordered grey accumulation generation theory is valid, but also the model's prediction accuracy is higher, with the sample's average prediction accuracy being 93.662 per cent.

The method exposed in the paper can be used on soil organic matter content hyper‐spectral inversion and even for other similar forecast problems.

The paper succeeds in realising both prediction pattern and application of soil organic matter content hyper‐spectral inversion by using the newest developed theories: grey GM(0, N) model based on the ordered grey accumulation generation.

Discusses the 2‐D minimum free energy (MFE) parameter and spectral estimation method and presents an algorithm for its implementation. Notes a profound lack of results in the literature on 2‐D spectral estimation methods and on their comparison. To address this issue and to impart an overall impression of the performance of 2‐D MFE, compares results from the Levinson method, a maximum entropy method (MEM), and a hybrid method with 2‐D MFE. Points out that 2‐D MFE can provide superior spectral estimates to that produced with MEM and that, in general, MFE requires a larger area of correlation support than the hybrid method. Also notes that 2‐D MFE can provide superior spectral estimation over the 2‐D Levinson algorithm.

In the first part of this paper a new method of applying the Maximum Entropy Principle (MEP) is presented, which makes use of a “frequency related” entropy, and which is valid for all stationary processes. The method is believed valid only in the case of discrete spectra. In the second part of the paper, a method of estimating continuous spectra in the presence of noise is presented, which makes use of the Mutual Information Principle (MIP). Although the method proceeds smoothly in mathematical terms, there appear to be some difficulties in interpreting the physical meaning of some of the expressions. Examples in the use of both methods are presented, for the usual practical problem of estimating a power spectrum for a process whose autocorrelation function is partially known a priori.