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Weighing-In-Motion (WIM) technology is one of the main tools for pavement management. It can accurately describe the traffic situation on the road and minimize overload problems. WIM sensors are the core elements of the WIM system. The excellent basic performance of WIMs sensor and its ability to maintain a stable output under different temperature environments are critical to the entire process of WIM. In this study, a WIM sensor was developed, which adopted a PZT-5H piezoelectric ceramic and integrated a temperature probe into the sensor. The designed WIM sensor has the advantages of having a small size, simple structure, high sensitivity, and low cost. A sine loading test was designed to test the basic performance of the piezoelectric sensor by using amplitude scanning and frequency scanning. The test results indicated that the piezoelectric sensor exhibits a clear linear relationship between input load and output voltage under constant environmental temperature. The linear correlation coefficient R2 of the fitting line is up to 0.999, and the sensitivity is 4.04858 mV/N at a loading frequency of 2 Hz at room temperature. The sensor has good frequency-independent characteristics. However, the temperature has a significant impact on it. Therefore, the output performance of the piezoelectric ceramic sensor is stabilized under different temperature conditions by using a multivariate nonlinear fitting algorithm for temperature compensation. The fitting result R2 is 0.9686, the root mean square error (RMSE) is 0.2497, and temperature correction was achieved. This study has significant implications for the application of piezoelectric ceramic sensors in road WIM systems.

When talc is employed as a mineral raw material in ceramic and other material domains, it undergoes specific temperature conditions. Understanding its dehydroxylation mechanism is crucial for guiding the processing and preparation techniques of related materials. In this study, non-isothermal thermogravimetry (TG) and thermodilatometry (TD) techniques were utilized to investigate the dehydroxylation kinetics of Longsheng talc between 30 °C and 1200 °C using the NETZSCH STA409PC thermal analyzer and DIL402PC thermodilatometry analyzer. The derivative thermogravimetry (DTG) curve of talc reveals a three-stage dehydroxylation process, while the derivative thermodilatometry (DTD) curve indicates the existence of five stages within this process. The TD/DTD technology exhibits higher resolution than DTA–TG technology in revealing the complex dehydroxylation process of talc, due to maintaining the sample’s natural characteristics. With an increase in the heating rate, both the DTG and DTD peak areas increase, and the peak temperatures shift toward higher temperatures, suggesting that the dehydroxylation process is kinetically controlled. Under both non-isothermal methods, the activation energy values obtained through the Flynn–Wall–Ozawa (FWO) iso-conversational method exhibit variations with the reaction progress, indicating the presence of at least five reaction stages in talc dehydroxylation. Furthermore, under both non-isothermal methods, the talc’s most probable reaction mechanism model, determined through iterative optimization based on nonlinear regression equations, is in complete agreement (including the reaction pathway and reaction equation). This model follows a five-step competitive mechanism (p:f,f,c,f; F n -A n -F n -F n -A n ), with the third stage competing with the fourth and fifth stages. The results confirm that both non-isothermal techniques have their advantages in revealing the staged dehydroxylation of talc. The non-isothermal TG method offers better experimental operability and repeatability, while the non-isothermal TD technique better preserves the sample’s original natural state and provides higher resolution. Only when the two techniques complement and verify each other can they be beneficial for revealing the complex process of mineral dehydroxylation reaction.

Background Di-nitrogen oxide (N2O) emissions from soil may lead to nonpoint-source pollution in farmland. Improving the C and N content in the soil is an excellent strategy to reduce N2O emission and mitigate soil N loss. However, this method lacks a unified mathematical index or standard to evaluate its effect. Methods To quantify the impact of soil improvement (C and N) on N2O emissions, we conducted a 2-year field experiment using biochar as carbon source and fertilizer as nitrogen source, setting three treatments (fertilization (300 kg N ha−1), fertilization + biochar (30 t ha−1), control). Results Results indicate that after biochar application, the average soil water content above 20 cm increased by ∼26% and 26.92% in 2019, and ∼10% and 12.49% in 2020. The average soil temperature above 20 cm also increased by ∼2% and 3.41% in 2019. Fertigation significantly promotes the soil N2O emissions, and biochar application indeed inhibited the cumulation by approximately 52.4% in 2019 and 33.9% in 2020, respectively. N2O emissions strongly depend on the deep soil moisture and temperature (20–80 cm), in addition to the surface soil moisture and temperature (0–20 cm). Therefore, we established an exponential model between the soil moisture and N2O emissions based on theoretical analysis. We find that the N2O emissions exponentially increase with increasing soil moisture regardless of fertilization or biochar application. Furthermore, the coefficient a < 0 means that N2O emissions initially increase and then decrease. The aRU < aCK indicates that fertilization does promote the rate of N2O emissions, and the aBRU > aRU indicates that biochar application mitigates this rate induced by fertilization. This conclusion can be verified by the sensitivity coefficient (SCB of 1.02 and 14.74; SCU of 19.18 and 20.83). Thus, we believe the model can quantify the impact of soil C and N changes on N2O emissions. We can conclude that biochar does significantly reduce N2O emissions from farmland.

Marine risers are essential for offshore resource extraction, yet traditional metal risers encounter limitations in deep-sea applications due to their substantial weight. Fiber-reinforced polymer (FRP) composites offer a promising alternative with advantages including low density and enhanced corrosion/fatigue resistance. However, FRP risers remain susceptible to fatigue damage from vortex-induced vibration (VIV). Therefore, this study investigated VIV behavior of FRP composite risers considering the coupled effect of tensile-flexural moduli, top tensions, slenderness ratios, and flow velocities. Through an orthogonal experimental design, eighteen cases were analyzed using multivariate nonlinear fitting. Results indicated that FRP composite risers exhibited larger vibration amplitudes than metal counterparts, with amplitudes increasing to both riser length and flow velocity. It was also found that the optimized FRP configuration demonstrated enhanced fiber strength utilization. Parameter coupling analysis revealed that the multivariate nonlinear fitting model achieved sufficient accuracy when incorporating two coupled parameters, with the most significant interaction occurring between flexural modulus and top tension.

In a sensor array system with the ability to design multiple sensor elements, selecting the optimal sensor elements can maximize the efficiency of the sensor array in responding to various analytes. This paper proposes the application of hard chemical modeling as a means to identify the optimal subset of indicator displacement assay (IDA)-based sensors in the array, aiming to achieve maximum performance for detection or quantification. The model governing all reactions in the IDA sensor and the model of the pure spectrum of active species are first determined. Next, by applying the model of the pure spectrum of active species (including the indicator and indicator-receptor complex) to each sensor element and taking into account the system’s nonlinearity, corrected concentration profiles of active species are derived using the generalized classical least square (G-CLS) method. These corrected concentration profiles are utilized as the output signal for each sensor element. Finally, the dynamic ranges (DR) of each sensor element and subsequently the DR for all possible sensor arrays are determined. To assess the effectiveness of the sensor array through dynamic range analysis, an IDA-based sensor system comprising five different elements was designed. It was observed that sensors with a larger dynamic range, when arranged together in an array, are more efficient for the quantitative identification of analytes. However, simply increasing the number of elements in the sensor array may not necessarily enhance its effectiveness; instead, it could amplify the noise within the system. Additionally, multivariate fitting regression with Gaussian function (MFRG), a nonlinear calibration method, was applied to assess the prediction ability of all possible designed sensor arrays. Graphical abstract

Realizing the integration of intelligent fruit picking and grading for apple harvesting robots is an inevitable requirement for the future development of smart agriculture and precision agriculture. Therefore, an apple maximum diameter estimation model based on RGB-D camera fusion depth information was proposed in the study. Firstly, the maximum diameter parameters of Red Fuji apples were collected, and the results were statistically analyzed. Then, based on the Intel RealSense D435 RGB-D depth camera and LabelImg software, the depth information of apples and the two-dimensional size information of fruit images were obtained. Furthermore, the relationship between fruit depth information, two-dimensional size information of fruit images, and the maximum diameter of apples was explored. Based on Origin software, multiple regression analysis and nonlinear surface fitting were used to analyze the correlation between fruit depth, diagonal length of fruit bounding rectangle, and maximum diameter. A model for estimating the maximum diameter of apples was constructed. Finally, the constructed maximum diameter estimation model was experimentally validated and evaluated for imitation apples in the laboratory and fruits on the Red Fuji fruit trees in modern apple orchards. The experimental results showed that the average maximum relative error of the constructed model in the laboratory imitation apple validation set was ±4.1%, the correlation coefficient (R2) of the estimated model was 0.98613, and the root mean square error (RMSE) was 3.21 mm. The average maximum diameter estimation relative error on the modern orchard Red Fuji apple validation set was ±3.77%, the correlation coefficient (R2) of the estimation model was 0.84, and the root mean square error (RMSE) was 3.95 mm. The proposed model can provide theoretical basis and technical support for the selective apple-picking operation of intelligent robots based on apple size grading.

Forest resources are the most important natural resources; their dynamic changes (growth or decline) are affected by socio-economic factors, and to study their linkage is of great significance. However, the relationship between forest resources and social economic factors is normally a multivariate nonlinear relationship. There are difficulties in accurately analyzing it by using traditional multivariate-statistical methods. Also, its explicit mathematical model is inconvenient for intelligent management. In this paper, the radial basis function (RBF) neural network was introduced to study the relationship between the changes of forest resources and socio-economic factors and was evaluated by comparison with the traditional multiple-linear regression model. The results showed that the RBF neural network method can be applied in modeling the dynamic changes of forest resources and showed a higher prediction accuracy over the traditional statistical modeling approaches. At the same time, the RBF neural network can analyze and evaluate the importance of influencing factors simply and conveniently. The results provide a new way and show an application potential for the analysis and intelligent management in forest resources.

There is a plethora of non-linear models to describe bivariate relationships related to ecological, biological and environmental problems, and this makes difficult to have a general aspect about the suitable models for a new-born dataset. Additionally, there is a special interest for bivariate non-linear models which can describe the relative variation of the dependent variable (NLR models) (i.e. these models provide a restricted range of values between 0 and 1) because they can easily be adjusted to fit different datasets which describe the same relationship. The aim of this study is to provide a review and synthesis of NLR models which can be used to describe bivariate relationships which follow bell-shaped, simple-double sigmoid, bilinear and periodical patterns. This attempt aims to save time and effort for the selection of a NLR model based on five steps (a) preparation of data, (b) visual identification of the suitable model based on pre-constructed graphs, (c) a starting point using the simpler form (base function) of the selected models which are given in complex general forms, (d) directions to increase the number of coefficients in order to improve fitting and (e) techniques to modify the given NLR models in order to derive new ones with inverted patterns.

Malaria is one of the most severe problems faced by the world even today. Understanding the causative factors such as age, sex, social factors, environmental variability etc. as well as underlying transmission dynamics of the disease is important for epidemiological research on malaria and its eradication. Thus, development of suitable modeling approach and methodology, based on the available data on the incidence of the disease and other related factors is of utmost importance. In this study, we developed a simple non-linear regression methodology in modeling and forecasting malaria incidence in Chennai city, India, and predicted future disease incidence with high confidence level. We considered three types of data to develop the regression methodology: a longer time series data of Slide Positivity Rates (SPR) of malaria; a smaller time series data (deaths due to Plasmodium vivax) of one year; and spatial data (zonal distribution of P. vivax deaths) for the city along with the climatic factors, population and previous incidence of the disease. We performed variable selection by simple correlation study, identification of the initial relationship between variables through non-linear curve fitting and used multi-step methods for induction of variables in the non-linear regression analysis along with applied Gauss-Markov models, and ANOVA for testing the prediction, validity and constructing the confidence intervals. The results execute the applicability of our method for different types of data, the autoregressive nature of forecasting, and show high prediction power for both SPR and P. vivax deaths, where the one-lag SPR values plays an influential role and proves useful for better prediction. Different climatic factors are identified as playing crucial role on shaping the disease curve. Further, disease incidence at zonal level and the effect of causative factors on different zonal clusters indicate the pattern of malaria prevalence in the city. The study also demonstrates that with excellent models of climatic forecasts readily available, using this method one can predict the disease incidence at long forecasting horizons, with high degree of efficiency and based on such technique a useful early warning system can be developed region wise or nation wise for disease prevention and control activities.

The performance of the F test in identifying the correct number of components in exponential functions is investigated by mathematical and computational techniques. Uncoupled systems can be most easily identified when the relaxation times are widely separated but the exponential functions encountered in pharrnacokinetics and biochemistry are linked in that the amplitudes and eigenvalues are not independent. In such systems correct model discrimination occurs as the relaxation times become closer together. The possibility of nonreal eigenvalues is emphasized and an enzyme kinetic model with this property is investigated.