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Non-equidistant GM(1,1) (abbreviated as NEGM) model is widely used in building settlement prediction because of its high accuracy and outstanding adaptability. To improve the building settlement prediction accuracy of the NEGM model, the fractional-order non-equidistant GM(1,1) model (abbreviated as FNEGM) is established in this study. In the modeling process of the FNEGM model, the fractional-order accumulated generating sequence is extended based on the first-order accumulated generating sequence, and the optimal parameters that increase the prediction precision of the model are obtained by using the whale optimization algorithm. The FNEGM model and the other two grey prediction models are applied to three cases, and five prediction performance indexes are used to evaluate the prediction precision of the three models. The results show that the FNEGM model is more suitable for predicting the settlement of buildings than the other two grey prediction models.

A study was carried out to investigate the release of volatile organic compounds (VOCs) during drying of plantation Pinus sylvestris grown in China and naturally grown Pinus sylvestris from Russia. Our purpose was to provide basic information that can help wood processing mills set their VOCs emission limits and control the exhaust gas within such limits. During conventional drying of the plantation Pinus sylvestris, a total of 22 chemical compounds were detected in the exhaust gas: 9 aldehydes including formaldehyde, 8 terpenes including α-pinene, and 3 additional compounds including alkane, and propylbenzene. The VOCs released during both conventional drying and high-temperature drying were the same. However, large amounts of benzene were detected during the high-temperature drying process. During conventional drying of the Russian Pinus sylvestris material, a total of 17 chemical compounds were detected: 7 aldehydes including formaldehyde, 6 terpenes including α-pinene, and 2 additional compounds. The VOCs released during conventional drying and high-temperature drying were the same. However, large amounts of camphene were detected during high-temperature drying. For plantation Pinus sylvestris, the release of VOCs primarily took place at the later stage of conventional drying, and at the earlier stage of high-temperature drying. For Russian Pinus sylvestris, the amount and the release rate of VOCs during conventional drying were extremely low, and the VOCs during high-temperature drying were primarily released at the later stage. The total amount of VOCs released during drying was much higher from the plantation Pinus sylvestris than from Russian Pinus sylvestris material.

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Aiming at the problem of unstable prediction accuracy of the classic NGM (1, 1, k) model, the modeling principle and parameter estimation method of this model are deeply analyzed in this study. Taking the minimum mean absolute percentage error as the objective function, the model is improved from the two perspectives of the construction method of the background value and the fractional order accumulation generation. The fractional order accumulation NGM (1, 1, k) model based on the optimal background value (short for the FBNGM (1, 1, k) model) is proposed in the study. The particle swarm optimization algorithm is used to estimate the parameters of the proposed model. Taking two actual cases with economic significance as examples, empirical analysis of the proposed model is conducted. The simulation and prediction results show the practicality and efficiency of the FBNGM (1, 1, k) model proposed in this study, which further broadens the application scope of the grey prediction model.