Some non-linear height–diameter models performance for mixed stand in forests in Northwest Iran

This study evaluated the total height of trees based on diameter at breast height by using 23 widely used height-diameter non-linear regression models for mixed-species forest stands consisting of Caucasian oak,field maple,and hornbeam from forests in Northwest Iran.1920 trees were measured in 6 sampling plots(every sampling plot has 1 ha area).The fit of the best height–diameter models for each species were compared based on R2,Root Mean Square Error(RMSE),Akaike information criterion(AIC),standard error,and relative ranking performance criteria.In the final step,verification of results was performed by paired sample t-test to compare the observed height and estimated height.Results showed that among 23 height-diameter models,the best models were obtained from the top five ones including Modified-logistic,Prodan,Sibbesen,Burkhart,and Exponential.Comparison between the actual observed height and estimated height for Caucasian oak showed that Modified–Logistic,Prodan,Sibbesen,Burkhart,and Exponential performed better than the others,respectively(There were no statistically significant differences between observed heights and predicted height(p≥0.05)).Prodan,Modified-Logistic,Burkhart,and Loetch evaluated field maple tree height correctly,and Modified-Logistic,Burkhart,and Loetch had better fitness compared to the others for hornbeam,respectively.Although other models were introduced as appropriate criteria,they could not reliably predict the height of trees.Using the Rank analysis,the Modified-Logistic model for the Caucasian oak and Prodan model for field maple and hornbeam had the best performance.Finally,to complement the results of this study,it is suggested to assess how environmental factors such as elevation,climate parameters,forest protection policy and forest structure will modify height-diameter allometry models and will enhance the prediction accuracy of tree heights prediction in mixed stands.

Influence of Confined Concrete Models on the Seismic Response of RC Frames

In this study, the influence of confined concrete models on the response of reinforced concrete structures is investigatedat member and global system levels. The commonly encountered concrete models such as Modified Kent-Park, Saatçioğlu-Razvi, and Mander are considered. Two moment-resisting frames designed according to thepre-modern code are taken into consideration to reflect the example of an RC moment-resisting frame in thecurrent building stock. The building is in an earthquake-prone zone located on Z3 Soil Type. The inelasticresponse of the building frame is modelled by considering the plastic hinges formed on each beam and columnelement for different concrete classes and stirrups spacings. The models are subjected to non-linear static analyses.The differences between confined concrete models are comparatively investigated at both reinforced concretemember and system levels. Based on the results of the comparative analysis, it is revealed that the column behaviouris mostly influenced by the choice of model, due to axial loads and confinement effects, while the beams areless affected, and also it is observed that the differences exhibited in the moment-curvature response of columncross-sections do not significantly affect the overall behaviour of the global system. This highlights the critical roleof model selection relative to the concrete strength and stirrup spacing of the member.

Heavy metals adsorption by banana peels micro-powder: Equilibrium modeling by non-linear models

In this study the copper and lead adsorption efficiency onto banana peels powder was investigated. The agroindustrial waste recovery represents one of the Circular Economy pillars. In the view of the synthesis of an environmentally friendly adsorbent material, the powder was used without any preliminary chemical or thermal activation, but only after simple washing, drying and grinding. The bio-adsorbent was characterized by the FTIR technique and tested in batch mode on synthetic aqueous solutions containing Pb and Cu in the range 10–90 mg·L^(-1). A selection of two(Langmuir, Freundlich) and three(Sips, Redlich–Peterson, Koble–Corrigan) parameter isotherm models was chosen to fit adsorption equilibrium data by non-linear regression procedure. The best fit isotherm model was selected relying on the error function with the lowest average percentage error(APE) value, among those characterized by the highest R^2 values. As expected, the three-parameter models are found to better represent both metals bio-adsorption, with APE and R^2 values always lower and higher, respectively, than the corresponding values obtained for the two-parameter models.

Processing Approach of Non-linear Adjustment Models in the Space of Non-linear Models

This paper investigates the mathematic features of non-linear models and discusses the processing way of non-linear factors which contributes to the non-linearity of a non-linear model. On the basis of the error definition,this paper puts forward a new adjustment criterion, SGPE.Last,this paper investigates the solution of a non-linear regression model in the non-linear model space and makes the comparison between the estimated values in non-linear model space and those in linear model space.

Stochastic Models to Mitigate Sparse Sensor Attacks in Continuous-Time Non-Linear Cyber-Physical Systems

Cyber-Physical Systems are very vulnerable to sparse sensor attacks.But current protection mechanisms employ linear and deterministic models which cannot detect attacks precisely.Therefore,in this paper,we propose a new non-linear generalized model to describe Cyber-Physical Systems.This model includes unknown multivariable discrete and continuous-time functions and different multiplicative noises to represent the evolution of physical processes and randomeffects in the physical and computationalworlds.Besides,the digitalization stage in hardware devices is represented too.Attackers and most critical sparse sensor attacks are described through a stochastic process.The reconstruction and protectionmechanisms are based on aweighted stochasticmodel.Error probability in data samples is estimated through different indicators commonly employed in non-linear dynamics(such as the Fourier transform,first-return maps,or the probability density function).A decision algorithm calculates the final reconstructed value considering the previous error probability.An experimental validation based on simulation tools and real deployments is also carried out.Both,the new technology performance and scalability are studied.Results prove that the proposed solution protects Cyber-Physical Systems against up to 92%of attacks and perturbations,with a computational delay below 2.5 s.The proposed model shows a linear complexity,as recursive or iterative structures are not employed,just algebraic and probabilistic functions.In conclusion,the new model and reconstructionmechanism can protect successfully Cyber-Physical Systems against sparse sensor attacks,even in dense or pervasive deployments and scenarios.

Power Allocation for Wireless Powered MIMO Transmissions with Non-Linear RF Energy Conversion Models

We study a radio frequency(RF) wireless energy transfer(WET) enabled multiple input multiple output(MIMO) system. A time slotted transmission pattern is considered. Each slot can be divided into two phases, downlink(DL) WET and uplink(UL) wireless information transmission(WIT). Since energy conversion efficiency of the energy harvesting circuits are non.linear, the conventional linear model leads to a mismatch for resource allocation. In this paper, the power allocation algorithm considering the practical non.linear energy harvesting circuits is studied. The optimization problem is formulated to maximize the energy efficiency of system with multiple constraints, i.e., the transmission power, the received power and the minimum harvested energy, which is a non.convex problem. We transform the objective function from fractional form into an equivalent objective function in subtractive form and provide an iterative power allocation algorithm to achieve the optimal solution. Numerical results show that our proposed algorithm with the non.linear RF energy conversion models can achieve much better performance than the algorithm with the conventional linear model.

Prosthetic modeling for femoral head based on ellipsoid fitting

A novel modeling method which can restore the shape of the femoral head with collapse induced by ischemic necrosis is proposed. First, sequential tomograms of the hip are obtained from a CT scan; secondly, an accurate and automatic method is used to extract the profile of the acetabulum; thirdly, a hybrid method is utilized to gather fiducial marks on the acetabulum; fourthly, bulky error sampling points are removed. Finally, an ellipsoid fitting method is used to fit the ellipsoid model of the femoral head. Two male sufferers with different necrosis extents are chosen as experimental subjects for contrastive simulation. Fifty cases of different ages （from 25 to 79 years old） are utilized for statistical comparisons of matching errors. The prosthetic models highly resemble the primary shape of the femoral head in health. This new method provides not only a theoretical model for accurate operation position fixing in an orthopaedics clinic, but it is also an innovative practical means for the individual manufacture of artificial femoral heads.

The forward and inverse problem of cardiac magnetic fields based on concentric ellipsoid torso-heart model

This paper constructs a concentric ellipsoid torso-heart model by boundary element method and investigates the impacts of model structures on the cardiac magnetic fields generated by both equivalent primary source--a current dipole and volume currents. Then by using the simulated magnetic fields based on torso-heart model as input, the cardiac current sources--an array of current dipoles by optimal constrained linear inverse method are constructed. Next, the current dipole array reconstruction considering boundaries is compared with that in an unbounded homogeneous medium. Furthermore, the influence of random noise on reconstruction is also considered and the reconstructing effect is judged by several reconstructing parameters.

A Hybrid Neural Network and Box-Jenkins Models for Time Series Forecasting

Time series forecasting plays a significant role in numerous applications,including but not limited to,industrial planning,water consumption,medical domains,exchange rates and consumer price index.The main problem is insufficient forecasting accuracy.The present study proposes a hybrid forecastingmethods to address this need.The proposed method includes three models.The first model is based on the autoregressive integrated moving average(ARIMA)statistical model;the second model is a back propagation neural network(BPNN)with adaptive slope and momentum parameters;and the thirdmodel is a hybridization between ARIMA and BPNN(ARIMA/BPNN)and artificial neural networks and ARIMA(ARIMA/ANN)to gain the benefits of linear and nonlinearmodeling.The forecasting models proposed in this study are used to predict the indices of the consumer price index(CPI),and predict the expected number of cancer patients in the Ibb Province in Yemen.Statistical standard measures used to evaluate the proposed method include(i)mean square error,(ii)mean absolute error,(iii)root mean square error,and(iv)mean absolute percentage error.Based on the computational results,the improvement rate of forecasting the CPI dataset was 5%,71%,and 4%for ARIMA/BPNN model,ARIMA/ANN model,and BPNN model respectively;while the result for cancer patients’dataset was 7%,200%,and 19%for ARIMA/BPNNmodel,ARIMA/ANN model,and BPNNmodel respectively.Therefore,it is obvious that the proposed method reduced the randomness degree,and the alterations affected the time series with data non-linearity.The ARIMA/ANN model outperformed each of its components when it was applied separately in terms of increasing the accuracy of forecasting and decreasing the overall errors of forecasting.

Quadratic and cubic eddy-viscosity models in turbulent supercavitating flow computation

Quadratic and cubic non-linear eddy-viscosity turbulence models(NLEVM) with low Reynolds number(Re) correction were presented to provide better description of anisotropic turbulence stresses in the numerical prediction of supercavitating flows,which are accompanied with large density ratio and large-scaled swirling flow structures.The applications of the NLEVM were carried out through a self-developed cavitation codes,coupled with a cavitation model based on the transport equation of liquid phase.These NLEVM were verified capable of capturing more accurate macroscopic shape and hydrodynamic property of supercavity by the benchmark problems of supercavities over simple objects.Finally,the cubic NLEVM was further applied to the numerical prediction of supercavitating flow around a complex submerged vehicle.The corresponding cavitation behaviors were explored in detail to provide beneficial experience for further research.

Non-Linear Mathematical Model of the Interaction between Tumor and Oncolytic Viruses

A mathematical modeling of tumor therapy with oncolytic viruses is discussed. The model consists of two coupled, deterministic differential equations allowing for cell reproduction and death, and cell infection. The model is one of the conceptual mathematical models of tumor growth that treat a tumor as a dynamic society of interacting cells. In this paper, we obtain an approximate analytical expression of uninfected and infected cell population by solving the non-linear equations using Homotopy analysis method (HAM). Furthermore, the results are compared with the numerical simulation of the problem using Matlab program. The obtained results are valid for the whole solution domain.

A Statistical Model with Non-Linear Effects and Non-Proportional Hazards for Breast Cancer Survival Analysis

The Cox proportional hazard model is being used extensively in oncology in studying the relationship between survival times and prognostic factors. The main question that needs to be addressed with respect to the applicability of the Cox PH model is whether the proportional hazard assumption is met. Failure to justify the subject assumption will lead to misleading results. In addition, identifying the correct functional form of the continuous covariates is an important aspect in the development of a Cox proportional hazard model. The purpose of this study is to develop an extended Cox regression model for breast cancer survival data which takes non-proportional hazards and non-linear effects that exist in prognostic factors into consideration. Non-proportional hazards and non-linear effects are detected using methods based on residuals. An extended Cox model with non-linear effects and time-varying effects is proposed to adjust the Cox proportional hazard model. Age and tumor size were found to have nonlinear effects. Progesterone receptor assay status and age violated the proportional hazard assumption in the Cox model. Quadratic effect of age and progesterone receptor assay status had hazard ratio that changes with time. We have introduced a statistical model to overcome the presence of the proportional hazard assumption violation for the Cox proportional hazard model for breast cancer data. The proposed extended model considers the time varying nature of the hazard ratio and non-linear effects of the covariates. Our improved Cox model gives a better insight on the hazard rates associated with the breast cancer risk factors.

Adjustment Model and Algorithm Based on Ellipsoid Uncertainty

In surveying adjustment models,there is usually some uncertain additional information or prior information on parameters,which can constrain the parameters,and guarantee the uniqueness and stability of parameter solution.In this paper,we firstly use ellipsoidal sets to describe uncertainty,and establish a new adjustment model with ellipsoidal uncertainty.Furthermore,we give a new adjustment criterion based on minimization trace of an outer ellipsoid with two ellipsoid intersections,and analyze the propagation law of uncertainty.Correspondingly,we give a new algorithm for the adjustment model with ellipsoid uncertainty.Finally,we give three examples to test and verify the effectiveness of our algorithm,and illustrate the relation between our result and the weighted mixed estimation.

Load Frequency Control of Small Hydropower Plants Using One-Input Fuzzy PI Controller with Linear and Non-Linear Plant Model

This study presents an intelligent approach for load frequency control (LFC) of small hydropower plants (SHPs). The approach which is based on fuzzy logic (FL), takes into account the non-linearity of SHPs—something which is not possible using traditional controllers. Most intelligent methods use two- input fuzzy controllers, but because such controllers are expensive, there is economic interest in the relatively cheaper single-input controllers. A non- linear control model based on one-input fuzzy logic PI (FLPI) controller was developed and applied to control the non-linear SHP. Using MATLAB/Si- mulink SimScape, the SHP was simulated with linear and non-linear plant models. The performance of the FLPI controller was investigated and compared with that of the conventional PI/PID controller. Results show that the settling time for the FLPI controller is about 8 times shorter;while the overshoot is about 15 times smaller compared to the conventional PI/PID controller. Therefore, the FLPI controller performs better than the conventional PI/PID controller not only in meeting the LFC control objective but also in ensuring increased dynamic stability of SHPs.

An Automated Model for Fitting a Hemi-Ellipsoid and Calculating Eigenvalues Using Matrices

Ellipsoid modeling is essential in a variety of fields, ranging from astronomy to medicine. Many response surfaces can be approximated by a hemi-ellipsoid, allowing estimation of shape, magnitude, and orientation via orthogonal vectors. If the shape of the ellipsoid under investigation changes over time, serial estimates of the orthogonal vectors allow time-sequence mapping of these complex response surfaces. We have developed a quantitative, analytic method that evaluates the dynamic changes of a hemi-ellipsoid over time that takes data points from a surface and transforms the data using a kernel function to matrix form. A least square analysis minimizes the difference between actual and calculated values and constructs the corresponding eigenvectors. With this method, it is possible to quantify the shape of a dynamic hemi-ellipsoid over time. Potential applications include modeling pressure surfaces in a variety of applications including medical.

General expression of double ellipsoidal heat source model and its error analysis

In order to analyze the maximum power density error with different heat flux distribution parameter values for double ellipsoidal heat source model, a general expression of double ellipsoidal heat source model was derived .front Goldak double ellipsoidal heat source model, and the error of maximum power density was analyzed under this foundation. The calculation error of thermal cycling parameters caused by the maximum power density error was compared quantitatively by numerical simulation. The results show that for guarantee the accuracy of welding numerical simulation, it is better to introduce an error correction coefficient into the Goldak double ellipsoidal heat source model expression. And, heat flux distribution parameter should get higher value for the higher power density welding methods.

Modelling Orthometric Heights from a Combination of Ellipsoidal Heights and Gravimetric Geoid Model in Rivers State, Nigeria

Many applications in geodesy, hydrography and engineering require geoid-related heights. Spirit leveling which is the traditional means of obtaining geoid- or mean sea level-related heights is slow, time-consuming and costly. Global Navigation Satellite Systems (GNSS) offer faster and relatively cheaper way of obtaining geoid-related heights when geoidal undulation is applied to ellipsoidal heights. However, difficulties involved in determining acceptable geoid height have seriously hampered the application of GNSS for leveling in Rivers State, thus necessitating the need to develop an acceptable geoid model which will serve as a means of conversion of GNSS-delivered ellipsoidal heights to their orthometric heights equivalent. In pursuance of this objective, a detailed gravimetric geoid has been evaluated for Rivers State, Nigeria. The computation of the geoid was carried out by the traditional remove-restore procedure. The Earth Geopotential Model 2008 (EGM08) was applied as the reference field for both the remove and restore parts of the procedures;spherical Fast Fourier Transform (FFT) was employed for the evaluation of the Molodenskii’s integral formula for the height anomaly, (ζ) to yield the quasi-geoid;while the Residual Terrain Modelling (RTM) was done by prism integration. The classical gravimetric geoid over Rivers State was obtained from the rigorously evaluated quasi-geoid by adding the quasi-geoid to geoid (N?- ζ) correction it. The minimum and maximum geoid height values are 18.599 m and 20.114 m respectively with standard deviation of 0.345 m across the study area. Comparison of the gravimetric geoidal heights with the GPS/Leveling-derived geoidal heights of 13 stations across Rivers State, Nigeria showed that the absolute agreement with respect to the GPS/leveling datum is generally better than 7 cm root mean squares (r.m.s) error. Results also showed that combining both GPS heights and the computed Rivers State geoid model can give orthometric heights accurate to 3 cm post-fit using a 4-parameter empirical model. The geoid model can thus serve as a good alternative to traditional leveling when used with GPS leveling, particularly for third order leveling in the study area.

Study on Duality of Wave and Particle of Turbulence Using CML Models

A family of coupled map lattice （CML） models has been developed to simulate the evolutional mechanism of interactions of convection, diffusion, and dispersion in both weakly and strongly coupled cases. Not only coherent and turbulent properties as well as their relations, but also the transitional states between convection dominating, diffusion dominating and dispersion dominating are analyzed to demonstrate the essential characteristics of any state. Numerical results show that the models are capable of simulating both layered coupling and stochastic mechanism, and lead us to understand whether or not turbulence coherent structure is formed by modulation of wave packet. The duality of wave and particle characters of turbulence is illustrated in the numerical simulation; a sketch picture is given to explain the questions associated with the turbulent inverse cascade, which is the result of the mutual interactions among the physical factors of nonlinearity, dissipation and dispersion.

THE MATHEMATICAL MODELS AND GENERALIZED VARIATIONAL PRINCIPLES OF NONLINEAR ANALYSIS FOR PERFORATED THIN PLATES

On foe basis of the Kirchoff-Karman hypothses for the nonlinear bending of thin plates, the three kinds of boundary value problems of nonlinear analysis for perforated fhin plates are presented under the differenr in-plane boundary conditions and the corresponding generalized varialional principles are established. One can see that all mathematical models presented in this paper are completely new ones and differ from the ordinary von Karman theory. These mathematical models can be applied to the nonlinear analysis and the Stability analysis of perforaled thin plates in arbitraryplane boundary conditions.

NON-LINEAR DYNAMIC MODEL RETRIEVAL OF SUBTROPICAL HIGH BASED ON EMPIRICAL ORTHOGONAL FUNCTION AND GENETIC ALGORITHM

Aiming at the difficulty of accurately constructing the dynamic model of subtropical high, based on the potential height field time series over 500 hPa layer of T106 numerical forecast products, by using EOF（empirical orthogonal function） temporal-spatial separation technique, the disassembled EOF time coefficients series were regarded as dynamical model variables, and dynamic system retrieval idea as well as genetic algorithm were introduced to make dynamical model parameters optimization search, then, a reasonable non-linear dynamic model of EOF time-coefficients was established. By dynamic model integral and EOF temporal-spatial components assembly, a mid-/long-term forecast of subtropical high was carried out. The experimental results show that the forecast results of dynamic model are superior to that of general numerical model forecast results. A new modeling idea and forecast technique is presented for diagnosing and forecasting such complicated weathers as subtropical high.