Traditional partial least squares regression (PLSR) and artificial neural networks (ANN) have been widely applied to estimate salt content from spectral reflectance in many different saline environments around the world. However, these methods entail a great amount of calculation, and their accuracy is low. To overcome these problems, a probability neural network (PNN) model based on particle swarm optimization was used in this study to build soil salt content models. Furthermore, there is a clear correlation between the level of human activities and the degree of salinization of an environment. This paper is the first to discuss this matter. Here, the performance of the PNN model to estimate soil salt content from reflectance data was investigated in areas non-affected (Area A) and affected (Area B) by human activities. The study area is located in Xingjinag, China. Different mathematical procedures, five wave band intervals, and two types of signal input sources were used for cross analysis. The coefficient of determination (R²), root mean square error (RMSE), and ratio of performance to deviation (RPD) index values were compared to verify the reliability of the model. Particle swarm optimization was used to adjust the optimal smoothing parameters of the PNN model and to avoid the long training processes required by the traditional ANN. The results show that the optimal wave band interval of the PNN is between 1000 nm and 1350 nm in Area A and between 400 nm and 700 nm in Area B. The reciprocal (1/R) transformation after Savitzky-Golay (SG) smoothing of the signal source is optimal for both areas. The RPD for both is greater than 30, which shows that the PNN model is applicable to areas with and without human activities and the prediction results are very good. The results indicated that the optimal wave band intervals for PNN modeling differed in areas affected and non-affected by human activities. The optimal interval of the artificial activities region falls in the visible light portion of the spectrum, and the optimized wave band region without human activities falls in the near-infrared short-wave portion of the spectrum.

Soil salinization is an ecological challenge across the world. Particularly in arid and semi-arid regions where evaporation is rapid and rainfall is scarce, both primary soil salinization and secondary salinization due to human activity pose serious concerns. Soil is subject to various human disturbances in Xinjiang in this area. Samples with a depth of 0–10 cm from 90 soils were taken from three areas: a slightly disturbed area (Area A), a moderately disturbed area (Area B), and a severely disturbed area (Area C). In this study, we first calculated the hyperspectral reflectance of five spectra (R, $\sqrt{\mathrm{R}}$, 1/R, lgR, 1/lgR, or original, root mean square, reciprocal, logarithm, and reciprocal logarithm, respectively) using different fractional-order differential (FOD) models, then extracted the bands that passed the 0.01 significance level between spectra and total salt content, and finally proposed a partial least squares regression (PLSR) model based on the FOD of the significance level band (SLB). This proposed model (FOD-SLB-PLSR) is compared with the other three PLSR models to predict with precision the total salt content. The other three models are All-PLSR, FOD-All-PLSR, and IOD-SLB-PLSR, which respectively represent PLSR models based on all bands, all fractional-order differential bands, and significance level bands of the integral differential. The simulations show that: (1) The optimal model for predicting total salt content in Area A was the FOD-SLB-PLSR based on a 1.6 order 1/lgR, which provided good predictability of total salt content with a RPD (ratio of the performance to deviation) between 1.8 and 2.0. The optimal model for predicting total salt content in Area B was a FOD-SLB-PLSR based on a 1.7 order 1/R, which showed good predictability for total salt content with RPDs between 2.0 and 2.5. The optimal model for predicting total salt content in Area C was a FOD-SLB-PLSR based on a 1.8 order lgR, which also showed good predictability for total salt content with RPDs between 2.0 and 2.5. (2) Soils subject to various disturbance levels had optimal FOD-SLB-PLSR models located in the higher fractional order between 1.6 and 1.8. This indicates that higher-order FODs have a stronger ability to extract feature data from complex information. (3) The optimal FOD-SLB-PLSR model for each area was superior to the corresponding All-PSLR, FOD-All-PLSR, and IOD-SLB-PLSR models in predicting total salt content. The RPD value for the optimal FOD-SLB-PLSR model in each area compared to the best integral differential model showed an improvement of 9%, 45%, and 22% for Areas A, B, and C, respectively. It further showed that the fractional-order differential model provides superior prediction over the integral differential. (4) The RPD values that provided an optimal FOD-SLB-PLSR model for each area were: Area A (1.9061) < Area B (2.0761) < Area C (2.2892). This indicates that the prediction effect of data processed by fractional-order differential increases with human disturbance increases and results in a higher-precision model.

Soil salinization is a global ecological and environmental problem in arid and semi-arid areas that can be ameliorated via soil management, visible-near infrared-shortwave infrared (VNIR-SWIR) spectroscopy can be adapted to rapidly monitor soil salinity content. This study explored the potential of Grünwald–Letnikov fractional-order derivative (FOD), feature band selection methods, nonlinear partial least squares regression (PLSR), and four machine learning models to estimate the soil salinity content using VNIR-SWIR spectra. Ninety sample points were field scanned with VNIR-SWR and soil samples (0–20 cm) were obtained at the time of scanning. The samples points come from three zones representing different intensities of human interference (I, II, and III Zones) in Fukang, Xinjiang, China. Each zone contained thirty sample points. For modeling, we firstly adopted FOD (with intervals of 0.1 and range of 0–2) as a preprocessing method to analyze soil hyperspectral data. Then, four sets of spectral bands (R-FOD-FULL indicates full band range, R-FOD-CC5 bands that met a 0.05 significance test, R-FOD-CC1 bands that met a 0.01 significance test, and R-FOD-CC1-CARS represents CC1 combined with competitive adaptive reweighted sampling) were selected as spectral input variables to develop the estimation model. Finally, four machine learning models, namely, generalized regression neural network (GRNN), extreme learning machine (ELM), random forest (RF), and PLSR, to estimate soil salinity. Study results showed that (1) the heat map of correlation coefficient matrix between hyperspectral data and salinity indicated that FOD significantly improved the correlation. (2) The characteristic band variables extracted and used by R-FOD-CC1 were fewer in number, and redundancy between bands smaller than R-FOD-FULL and R-FOD-CC5, thus estimation accuracy of R-FOD-CC1 was higher than R-FOD-CC5 or R-FOD-FULL. A high prediction accuracy was achieved with a less complex calculation. (3) The GRNN model yielded the best salinity estimation in all three zones compared to ELM, BPNN, RF, and PLSR on the whole, whereas, the RF model had the worst estimation effect. The R-FOD-CC1-CARS-GRNN model yielded the best salinity estimation in I Zone with R², RMSE and RPD of 0.7784, 1.8762, and 2.0568, respectively. The fractional order was 1.5 and estimation performance was great. The optimal model for predicting soil salinity in II and III Zone was, also, R-FOD-CC1-CARS-GRNN (R² = 0.7912, RMSE = 3.4001, and RPD = 1.8985 in II Zone; R² = 0.8192, RMSE = 6.6260, and RPD = 1.8190 in III Zone), with the fractional order of 1.7- and 1.6-, respectively, and the estimation performance were all fine. (4) The characteristic bands selected by the best model in I, II, and III Zones were 8, 9, and 11, respectively, which account for 0.45%, 0.51%, and 0.63%% of the full bands. This approach reduces the number of modeled band variables and simplifies the model structure.

Soluble salts in saline soil often exist in the form of salt base ions, and excessive water-soluble base ions can harm plant growth. As one of the water-soluble base ions, Na+ ion, is the main indicator of the degree of soil salinization. The pretreatment of visible, near infrared and short-wave infrared (VNIR-SWIR) spectroscopy data is the key to establishing a high-precision inversion model, and a proper pretreatment method can fully extract the effective information hidden in the hyperspectral data. Meanwhile, different degrees of human activity stress will have an impact on the ecological environment of oases. However, there are few comparative analyses of the data pretreatment effects for soil water-soluble base ions on the environment under different human interference conditions. Therefore, in this study, the difference in the degree of soil disturbance caused by human activities was used as the basis for dividing the experimental area into lightly disturbed area (Area A), moderately disturbed area (Area B) and severely disturbed zone (Area C). The Grünwald-Letnikov fractional-order derivative (FOD) was used to preprocess the VNIR-SWIR spectroscopic data measured by a FieldSpec®3Hi-Res spectrometer, which could fully extract the useful information hidden in the FOD of the VNIR-SWIR spectroscopy results and avoid the loss of information caused by the traditional integer-order derivative (1.0-order, 2.0-order) pretreatment. The spectrum pretreatment was composed of five transform spectra (R, $\sqrt{\mathrm{R}}$, 1/R, lgR, 1/lgR) and 21 FOD methods (step size is 0.1, derivative range is from 0.0- to 2.0-order). In addition, this manuscript compares and analyzes the pretreatment advantages between fractional-order and integer-order. The main results were as follows: (1) Grünwald-Letnikov FOD can reveal the nonlinear characteristics and variation laws of the field hyperspectral of saline soil, namely, due to the continuous performance of the order selection, the FOD accurately depicts the details of spectral changes during the derivation process, and improves the resolution between the peaks of the hyperspectral spectrum. (2) There is a big difference in the shape of the correlation coefficient curve between the original hyperspectral and Na+ at different FOD. The correlation coefficient curve has a clear outline in rang of the 0.0- to 0.6-order, and the change trend is gentle, which presents a certain gradual form. With the continuous increase of the order of the FOD, the change range of the correlation coefficient curve is gradually increased, and the fluctuation is greater between the 1.0-order and the 2.0-order. (3) Regardless of the transformation spectrum and different interference regions, the improvement effect of the FOD on the correlation between hyperspectral and Na+ is significantly better than that of the integer-order derivative. Comparative analysis shows that he percentage of increase of the former is more than 3%, and the highest is more than 17%.

In this study we used a non-autonomous Chua’s circuit, and the fractional Lorenz chaos system. This was combined with the Extension theory detection method to analyze the voltage signals. The bearing vibration signals, measured using an acceleration sensor, were introduced into the master and slave systems through a Chua’s circuit. In a chaotic system, minor differences can cause significant changes that generate dynamic errors. The matter-element model extension can be used to determine the bearing condition. Extension theory can be used to establish classical and sectional domains using the dynamic errors of the fault conditions. The results obtained were compared with those from discrete Fourier transform analysis, wavelet analysis and an integer order chaos system. The diagnostic rate of the fractional-order master and slave chaotic system could reach 100% if the fractional-order parameter adjustment was used. This study presents a very efficient and inexpensive method for monitoring the state of ball bearings.

Magnetic nulls are traditionally suggested as main points where energy dissipation occurs during reconnection. Such nulls have been widely observed in the diffusion region of standard reconnection following a two‐fluid picture, but have never been investigated in the thin current sheet of electron‐only reconnection. Recently, an electron‐only reconnection event was observed by the Magnetospheric Multiscale (MMS) mission in Earth's magnetosheath. The small separation of MMS spacecraft (∼7 km) provides a good opportunity to examine whether magnetic nulls exist in electron‐only reconnection. By utilizing the First‐Order Taylor Expansion method, we find a radial null in this event. Moreover, such nulls degenerate into X‐type nulls inside a reconnecting current sheet, suggesting that it's quasi 2D structure. By reconstructing the topology of this null, we can also estimate the reconnection rate of this electron‐only reconnection event and find it's time‐varying, suggesting it's an unsteady process. Our results are useful to further understand the process of electron‐only reconnection.