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This article investigates some statistical and probabilistic properties of general threshold bilinear processes. Sufficient conditions for the existence of a causal, strictly and weak stationary solution for the equation defining a self-exciting threshold superdiagonal bilinear S E T B L process are derived. Then it is shown that under well-specified hypotheses the higher-order moments of the SETBL process are finite. As a result, the skewness and kurtosis indexes are explicitly computed. The exact autocorrelation function is derived with an arbitrarily fixed number of regimes. Also, the covariance functions of the process and its powers are evaluated and the second (respectively, higher)-order structure is shown to be similar to that of a linear process. This implies that the considered process admits an ARMA representation. Finally, necessary and sufficient conditions for the invertibility and geometric ergodicity of a SETBL model are established. Some examples illustrate the obtained theoretical results. [ABSTRACT FROM AUTHOR]

Abstract.The bilinear model has been frequently used in fields like control theory and economics to model seismic data. In this article, time-functional variance (TFV) noises are embedded into a specific bilinear model. We propose a generalized autoregressive conditional heteroskedasticity-type maximum likelihood estimator (GMLE) with a sieve method and then provide various inferential techniques based on this GMLE. It is shown that under the finite fourth moment of errors, the GMLE is consistent and asymptotically normally distributed. A simulation study and analysis of real data are additionally carried out to evaluate GMLE’s finite sample performance. [ABSTRACT FROM AUTHOR]

Experiments with two factors are commonly analyzed using two-way analysis of variance, where testing significance of interaction is straightforward. However, using bilinear models, interaction can be analyzed further. The additive main effects and multiplicative interaction (AMMI) model uses singular value decomposition for partitioning interaction into multiplicative terms, such that the first terms typically account for a large portion of the sum of squares, whereas the last terms are of minor importance. This model is used extensively for analysis of genotype-by-environment interaction in multi-environment trials. A recurring question is how to determine the number of terms to retain in the model. If data is replicated, which is usually the case, the F R test can be used for this purpose. The simple parametric bootstrap method is another option, although this test was developed for unreplicated data. Since both of these tests of significance may be applied in cases with replication, researchers need advice on which of the methods to use. We discuss several statistical models and show that the two methods address different questions. [ABSTRACT FROM AUTHOR]

Understanding how different neuronal types connect and communicate is critical to interpreting brain function and behavior. However, it has remained a formidable challenge to decipher the genetic underpinnings that dictate the specific connections formed between neuronal types. To address this, we propose a novel bilinear modeling approach that leverages the architecture similar to that of recommendation systems. Our model transforms the gene expressions of presynaptic and postsynaptic neuronal types, obtained from single-cell transcriptomics, into a covariance matrix. The objective is to construct this covariance matrix that closely mirrors a connectivity matrix, derived from connectomic data, reflecting the known anatomical connections between these neuronal types. When tested on a dataset of Caenorhabditis elegans, our model achieved a performance comparable to, if slightly better than, the previously proposed spatial connectome model (SCM) in reconstructing electrical synaptic connectivity based on gene expressions. Through a comparative analysis, our model not only captured all genetic interactions identified by the SCM but also inferred additional ones. Applied to a mouse retinal neuronal dataset, the bilinear model successfully recapitulated recognized connectivity motifs between bipolar cells and retinal ganglion cells, and provided interpretable insights into genetic interactions shaping the connectivity. Specifically, it identified unique genetic signatures associated with different connectivity motifs, including genes important to cell-cell adhesion and synapse formation, highlighting their role in orchestrating specific synaptic connections between these neurons. Our work establishes an innovative computational strategy for decoding the genetic programming of neuronal type connectivity. It not only sets a new benchmark for single-cell transcriptomic analysis of synaptic connections but also paves the way for mechanistic studies of neural circuit assembly and genetic manipulation of circuit wiring.

Bearing is the key component of rotating machinery, so the rapid and accurate fault diagnosis of bearing is of great significance. As one of the most commonly used diagnostic ways, vibration analysis has been explored by many scholars. However, vibration signals are underutilized in most studies and the fault information is not sufficiently extracted, which will lead to the failure of achieving expected diagnostic accuracy. This paper proposes a multilevel feature fusion of multi-domain vibration signals method for bearing fault diagnosis. Vibration signals are converted into time domain, frequency domain and time–frequency domain for fault diagnosis to realize the full use of vibration signals. The bilinear model and multi-head attention are applied to the fine-grained fusion of features extracted from multi-domain vibration signals. Experiments are conducted on Paderborn bearing data set to verify the effectiveness of proposed method. Results show that the accuracy of proposed method is greatly improved, which is much higher than the other methods. [ABSTRACT FROM AUTHOR]

In the paper, the autoregressive moving average model for matrix time series (MARMA) is investigated. The properties of the MARMA model are investigated by using the conditional least square estimation, the conditional maximum likelihood estimation, the projection theorem in Hilbert space and the decomposition technique of time series, which include necessary and sufficient conditions for stationarity and invertibility, model parameter estimation, model testing and model forecasting.

The cracking resistance and durability of the ultra-high-performance concrete (UHPC) structure are directly affected by its tensile behaviour. A micro-analysis method was established to study the tensile behaviour of the UHPC before the appearance of visible cracks. The cooperative characteristic of the steel fibre and the cement matrix was taken as a research focus of the micro-analysis method. The random distribution of steel fibre was considered as normal distribution. Based on the micro-analysis method, the tensile behaviour of UHPC was divided into the elastic stage and micro-damage development stage. Other data sourced elsewhere were used to verify the feasibility of the micro-analysis method and the necessary data were tested using pure bending specimens to verify the theoretical model. The results show that the working mechanism of inner steel fibre can be described by the micro-analysis method. The bending test results of the UHPC at the elastic and the micro-damage development stage match the theoretical model. The tensile behaviour of the UHPC is dominated by the inner steel fibre and the contribution of the cement matrix can be ignored. A bilinear model is proposed to describe the tensile constitutive of UHPC before the appearance of visible cracks, and the limitations of each stage are 8.85 MPa and 12.36 MPa.

Copyright of Engineering Mechanics / Gongcheng Lixue is the property of Engineering Mechanics Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper, we deal with the frequency domain approach to describe some probabilistic properties of the GARCH (p , q) processes using the associated transfer functions which seem more informative. So, in the first part, we propose an appropriate bilinear representation of GARCH (p , q) model governed by a second-order Hermite polynomial with leading coefficient 1, and we give a necessary and sufficient condition for the causal and second-order stationary solution. In a second part, we establish the autocovariance and the associated spectral density function of such a representation, and for its squared version in terms of transfer functions. As a consequence, it is observed that the second-order properties are similar to an ARMA process with uncorrelated innovations and hence the resort to higher-order properties however becomes inevitable. Therefore, the explicit expressions of bispectral densities of the process and its squared version are given and several illustrative examples are emphasized. Our results are related to the work of Terdik (2000, §3) for the GARCH(1, 1) model. [ABSTRACT FROM AUTHOR]

In order to study the seismic behavior of tenon-mortise joints with different pin types, as well as the influence of three parameters such as tenon height, tenon thickness, and column diameter on the mechanical properties of tenon-mortise joints, in this study, finite element software modeling was used for the quasi-static analysis of tenon-mortise joints, and the seismic indexes such as hysteretic curve, skeleton curve,and energy dissipation capacity of three types of specimens were obtained. The results showed that the hysteresis curves of the three types of tenon-mortise joints penetrating pin showed obvious Z-shape, and the pinch effect was obvious .The bearing capacity of three types of tenon-mortise joints with penetrating pin under repeated load was not significantly different. The tenon height, tenon thickness and column diameter had significant influence on the bearing capacity of tenon-mortise joints. The bearing capacity of joint increased with the increasing of tenon thickness and column diameter, and increased first and then decreased with the increase of tenon height. According to the skeleton curve of tenon-mortise with penetrating pin, a bending moment-turning angle bilinear model of the joint was established, which explored the influence of tenon height, tenon thickness and column diameter on the model parameters. In the design of wood structures, the influence of the size change of tenonmortise on the mechanical properties of joints should be considered comprehensively. [ABSTRACT FROM AUTHOR]

Copyright of Electric Power is the property of Electric Power Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The rotational stiffness of the pocket-type connection used in system scaffolding to join horizontal members and vertical members was evaluated. To investigate the rotational stiffness of connections when subjected to bending moments in the downward, upward, and lateral rotation directions, load tests were performed on 30 specimens with cantilever specimens for each rotational direction. Results showed that failure shapes of pocket-type connections were different depending on the rotation direction. Owing to the differences in the failure phenomena, the maximum moment capacity of the upwardly rotated specimens was the largest, followed by that of the downwardly rotated specimens and the laterally rotated specimens in that order. Compared to the Eurocode 3 connection classification, the pocket-type connections correspond to semi-rigid connections when the rotation direction is downward or upward, and they can be considered nominal pin connections when the rotation direction is lateral. From the moment-rotation curves, it was concluded that the rotational stiffness of the pocket-type connections could be estimated as a bilinear model. [ABSTRACT FROM AUTHOR]

Phyllochron, the reciprocal of the leaf appearance rate, is a critical genetic parameter in crop models for predicting growth characteristics and yield. Previous studies have shown that existing observations and predictive algorithms do not adequately represent a broad range of cultivars and environments. Here, we conducted a series of experiments in the field to quantify and disentangle the effects of sowing date and cultivar on maize leaf collar appearance (LCA). A bilinear model was found to accurately fit maize LCA (R2 adj > 0.99); this model revealed a slower rate of LCA for the first leaves compared to the last leaves. Turning points in the model occurred between the 9.2th and the 13.1th leaf, nearly always below the ear leaf and around a leaf age index (LAI) of 60.0%. The phyllochron before the turning point (PHYLL Ⅰ) was significantly higher than the phyllochron after the turning point (PHYLL Ⅱ) for all three maize cultivars, and PHYLL Ⅰ was approximately two times higher than PHYLL Ⅱ on average. Both PHYLL Ⅰ and PHYLL Ⅱ were significantly affected by sowing date and cultivar. Variations in PHYLL Ⅰ and PHYLL Ⅱ indicated strong plasticity in maize phyllochron at different leaf ranks. The results of this study are critical for improvement of maize management practices and extend the applicability of phyllochron-collar measurements in crop models. • Bilinear models could accurately predict maize leaf appearance time. • Turning points consistently occurred when the leaf age index was 60.0%. • Phyllochron was greater in earlier leaves than in later leaves. [ABSTRACT FROM AUTHOR]

Visual Question Answering (VQA) about diseases is an essential feature of intelligent management in smart agriculture. Currently, research on fruit tree diseases using deep learning mainly uses single-source data information, such as visible images or spectral data, yielding classification and identification results that cannot be directly used in practical agricultural decision-making. In this study, a VQA model for fruit tree diseases based on multimodal feature fusion was designed. Fusing images and Q&A knowledge of disease management, the model obtains the decision-making answer by querying questions about fruit tree disease images to find relevant disease image regions. The main contributions of this study were as follows: (1) a multimodal bilinear factorized pooling model using Tucker decomposition was proposed to fuse the image features with question features: (2) a deep modular co-attention architecture was explored to simultaneously learn the image and question attention to obtain richer graphical features and interactivity. The experiments showed that the proposed unified model combining the bilinear model and co-attentive learning in a new network architecture obtained 86.36% accuracy in decision-making under the condition of limited data (8,450 images and 4,560k Q&A pairs of data), outperforming existing multimodal methods. The data augmentation is adopted on the training set to avoid overfitting. Ten runs of 10-fold crossvalidation are used to report the unbiased performance. The proposed multimodal fusion model achieved friendly interaction and fine-grained identification and decision-making performance. Thus, the model can be widely deployed in intelligent agriculture. [ABSTRACT FROM AUTHOR]

The National Judicial Examination of China is an essential examination for selecting legal practitioners. In recent years, people have tried to use machine learning algorithms to answer examination questions. With the proposal of JEC-QA (Zhong et al. 2020), the judicial examination becomes a particular legal task. The data of judicial examination contains two types, i.e., Knowledge-Driven questions and Case-Analysis questions. Both require complex reasoning and text comprehension, thus challenging computers to answer judicial examination questions. We propose Bilinear Convolutional Neural Networks and Attention Networks (BCA) in this paper, which is an improved version based on the model proposed by our team on the Challenge of AI in Law 2021 judicial examination task. It has two essential modules, Knowledge-Driven Module (KDM) for local features extraction and Case-Analysis Module (CAM) for the semantic difference clarification between the question stem and the options. We also add a post-processing module to correct the results in the final stage. The experimental results show that our system achieves state-of-the-art in the offline test of the judicial examination task.

Bilinear models such as low-rank and dictionary methods, which decompose dynamic data to spatial and temporal factor matrices are powerful and memory-efficient tools for the recovery of dynamic MRI data. Current bilinear methods rely on sparsity and energy compaction priors on the factor matrices to regularize the recovery. Motivated by deep image prior, we introduce a novel bilinear model, whose factor matrices are generated using convolutional neural networks (CNNs). The CNN parameters, and equivalently the factors, are learned from the undersampled data of the specific subject. Unlike current unrolled deep learning methods that require the storage of all the time frames in the dataset, the proposed approach only requires the storage of the factors or compressed representation; this approach allows the direct use of this scheme to large-scale dynamic applications, including free breathing cardiac MRI considered in this work. To reduce the run time and to improve performance, we initialize the CNN parameters using existing factor methods. We use sparsity regularization of the network parameters to minimize the overfitting of the network to measurement noise. Our experiments on free-breathing and ungated cardiac cine data acquired using a navigated golden-angle gradient-echo radial sequence show the ability of our method to provide reduced spatial blurring as compared to classical bilinear methods as well as a recent unsupervised deep-learning approach. [ABSTRACT FROM AUTHOR]

Modeling and recognizing events in complex systems through machine learning techniques is a challenging task. Especially if the model is constrained to be explainable and interpretable, while ensuring high levels of accuracy. In this paper, we adopt a bilinear logistic regression model in which the parameters are trained in a data-driven fashion on a real-world dataset of power grid failure data. The bilinear white-box model – grounded on a specific neural architecture – has been proven effective in classifying faulty states with a performance comparable to several classifiers in technical literature. Additionally, the low computational complexity of the bilinear model, in terms of the number of free parameters, allows gaining insights into the fault phenomenon correlating the events that impact the power grid (exogenous causes) with its constitutive characteristics, thence eliciting the relational information hidden in the data. The proposed model is also able to estimate a vulnerability vector that can be associated, as a suitable characteristic "label", to power grid components, opening the way, as will be deeply demonstrated in the following, not only to predictive maintenance programs or condition monitoring tasks but also to risk assessment and scenario analyses in line with the explainable AI paradigm. • Introduced a bilinear logistic regression model trained on real-world power grid failure data for grid reliability assessment. • Emphasized the role of explainable AI in power grid analysis, highlighting the interpretability of the proposed model. • Developed a method to estimate a vulnerability vector for power grid components and a deep analysis related to the computed weight correlation matrix. • Stressed the importance of semantic specification in modeling complex systems. [ABSTRACT FROM AUTHOR]

The rotational stiffness of the pocket-type connection used in system scaffolding to join horizontal members and vertical members was evaluated. To investigate the rotational stiffness of connections when subjected to bending moments in the downward, upward, and lateral rotation directions, load tests were performed on 30 specimens with cantilever specimens for each rotational direction. Results showed that failure shapes of pocket-type connections were different depending on the rotation direction. Owing to the differences in the failure phenomena, the maximum moment capacity of the upwardly rotated specimens was the largest, followed by that of the downwardly rotated specimens and the laterally rotated specimens in that order. Compared to the Eurocode 3 connection classification, the pocket-type connections correspond to semi-rigid connections when the rotation direction is downward or upward, and they can be considered nominal pin connections when the rotation direction is lateral. From the moment-rotation curves, it was concluded that the rotational stiffness of the pocket-type connections could be estimated as a bilinear model.

Fibre-reinforced polymers (FRP) are widely used to enhance the performance of structural elements of various materials, including timber. Measurements of reinforced beams mostly involve load-deflection relationships in order to experimentally verify mechanical improvements, while numerical simulations require material parameters for constitutive laws. In this study, a numerical method based on the classical beam theory is presented to inversely determine the elastic-plastic parameters of the timber material and the reinforcing FRP fabric using measurement data on full-scale composite beams. Data on bending tests of spruce beams obtained in a previous research stage are used to demonstrate the method. The method can provide material parameters for the full size composite structural element prepared under conditions relevant to actual design conditions, including the reinforcement preparation. It is found that the bilinear model is an adequate description for wood, and good agreement between simulated and measured data is obtained. Model material parameters are computed and presented for several specimens individually. [ABSTRACT FROM AUTHOR]

With the development of electric vehicles, more and more high requirements for the lightweight design on EV body are put forward. This paper aims to study a new structure, aluminum alloy mortise-and-tenon structure, which is used for lightweight EVs. Two new types on aluminium alloy MT-T joint specimens are designed and tested under low-cycle reciprocating loading. And the failure characteristics, hysteretic curve, skeleton curve, restoring force model and energy dissipation curve are obtained by analyzing the experimental data. Moment and rotation angle relationship is conducted by joint geometric deformation and equilibrium relation. Based on theoretical model, a simplified bilinear model has been proposed for engineering calculation. When the beam bending performance is qualitatively analyzed, the theoretical model, simulation model and bilinear model are verified through experiments and finite element method simulations. The results show that mortise-and-tenon T joint main failure modes are plastic deformation caused by the upper contact area squeezed each other and the lower contact area divorced each other. Furthermore, it can be obtained from the theoretical model that MT-T joint deformation process consists of elastic segment and elastoplastic segment. Theoretical model, simulation model and bilinear model agree well with the experimental results. This fruit gives a useful reference to composite material used in EVs.

Understanding how different neuronal types connect and communicate is critical to interpreting brain function and behavior. However, it has remained a formidable challenge to decipher the genetic underpinnings that dictate the specific connections formed between neuronal types. To address this, we propose a novel bilinear modeling approach that leverages the architecture similar to that of recommendation systems. Our model transforms the gene expressions of presynaptic and postsynaptic neuronal types, obtained from single-cell transcriptomics, into a covariance matrix. The objective is to construct this covariance matrix that closely mirrors a connectivity matrix, derived from connectomic data, reflecting the known anatomical connections between these neuronal types. When tested on a dataset of Caenorhabditis elegans , our model achieved a performance comparable to, if slightly better than, the previously proposed spatial connectome model (SCM) in reconstructing electrical synaptic connectivity based on gene expressions. Through a comparative analysis, our model not only captured all genetic interactions identified by the SCM but also inferred additional ones. Applied to a mouse retinal neuronal dataset, the bilinear model successfully recapitulated recognized connectivity motifs between bipolar cells and retinal ganglion cells, and provided interpretable insights into genetic interactions shaping the connectivity. Specifically, it identified unique genetic signatures associated with different connectivity motifs, including genes important to cell-cell adhesion and synapse formation, highlighting their role in orchestrating specific synaptic connections between these neurons. Our work establishes an innovative computational strategy for decoding the genetic programming of neuronal type connectivity. It not only sets a new benchmark for single-cell transcriptomic analysis of synaptic connections but also paves the way for mechanistic studies of neural circuit assembly and genetic manipulation of circuit wiring., Competing Interests: MQ No competing interests declared, (© 2023, Qiao.)

Hysteresis is a common phenomenon arising in many engineering applications. It describes a memory-based relation between the restoring force and the displacement. Identification of the hysteretic parameters is central to practical application of the hysteretic models. To proceed so, a noteworthy thing is that the hysteretic models are often complex and non-differentiable so that getting the gradients is never straightforward and therefore, the swarm-based algorithm is often preferable to inverse hysteretic parameter identification. Along these lines, an improved artificial bee colony algorithm is developed in this paper for general hysteretic parameter identification. On the one hand, several hysteretic models along with the extensions to tackle the degradation and pinching behaviours are considered and how to model a structure with hysteretic components is also elaborated. As a result, the governing equation for the direct problem is established. On the other hand, the differential evolution mechanism is introduced to improve the original artificial bee colony algorithm. Numerical examples are conducted to testify the feasibility and accuracy of the proposed method in nonlinear hysteretic parameter identification. [ABSTRACT FROM AUTHOR]

Few-shot semantic segmentation remains an open problem because limited support (training) images are insufficient to represent the diverse semantics within target categories. Conventional methods typically model a target category solely using information from the support image(s), resulting in incomplete semantic activation. In this paper, we propose a novel few-shot segmentation approach, termed harmonic feature activation (HFA), with the aim to implement dense support-to-query semantic transform by incorporating the features of both query and support images. HFA is formulated as a bilinear model, which takes charge of the pixel-wise dense correlation (bilinear feature activation) between query and support images in a systematic way. HFA incorporates a low-rank decomposition procedure, which speeds up bilinear feature activation with negligible performance cost. In addition, a semantic diffusion procedure is fused with HFA, which further improves the global harmony and local consistency of the feature activation. Extensive experiments on commonly used datasets (PASCAL VOC and MS COCO) show that HFA improves the state-of-the-arts with significant margins. Code is available at https://github.com/Bibikiller/HFA. [ABSTRACT FROM AUTHOR]

Previous studies show that the indoor environment quality (IEQ) of buildings directly affects human health and comfort. This study aims to predict the change of indoor parameters at the next moment under the influences of the current indoor climate and outdoor climate and control the IEQ parameters based on the human thermal adaption in advance. We combine the simulation and the mathematical method to establish the office building model with air-conditioning and lighting systems and construct the bilinear model of the IEQ parameters and control variables. Unknown parameters are identified using the experimental method. Model predictive control (MPC) based on human thermal comfort is discussed by considering human thermal adaptation, and the neutral temperature is calculated through the dynamic relationship between outdoor and indoor temperatures. Results show that the temperature setpoint is adjusted in accordance with human adaptability, and the air-conditioning, fan, and lighting systems are controlled via MPC. The usage time of air-conditioning and light is reduced, and thus, energy is saved. [ABSTRACT FROM AUTHOR]

Robust control techniques for power converters are becoming more attractive because they can meet with most demanding control goals like uncertainties. In this sense, the Takagi-Sugeno (T-S) fuzzy controller based on linear matrix inequalities (LMI) is a linear control by intervals that has been relatively unexplored for the output-voltage regulation problem in switching converters. Through this technique it is possible to minimize the disturbance rejection level, satisfying constraints over the decay rate of state variables as well as the control effort. Therefore, it is possible to guarantee, a priori, the stability of the large-signal converters in a broad operation domain. This work presents the design of a fuzzy control synthesis based on a T-S fuzzy model for non-minimum phase dc-dc converters, such as boost and buck-boost. First, starting from the canonical bilinear converters expression, a Takagi-Sugeno (T-S) fuzzy model is obtained, allowing to define the fuzzy controller structure through the parallel distributed compensation technique (PDC). Finally, the fuzzy controller design based on LMIs is solved for the defined specification in close loop through MATLAB toolbox LMI. Simulations and experimental results of a 60 W prototype are presented to verify theoretical predictions. [ABSTRACT FROM AUTHOR]

• A general sensitivity-based framework is developed for nonlinear breathing crack identification. • The proposed approach is able to identify both locations and extents of the breathing cracks in a structure. • The smoothing strategy is shown feasible for sensitivity analysis of the non-differentiable bilinear breathing crack models. • The present approach is found insensitive to measurement noise. Breathing cracks are often encountered in engineering structures and detection of such cracks at the earliest stage is important for safety and serviceability of the structures. In this paper, a new breathing crack identification approach based on the time-domain sensitivity analysis is proposed. For the forward problem, the crack is simply treated as a nonlinear oscillator and how to model a structure with breathing cracks is specified. As regards the inverse crack identification, it is formulated as a nonlinear least-squares optimization problem and a new sensitivity-based approach is developed to get the solution. In doing so, the sensitivity analysis of the possibly non-differentiable breathing crack models is necessarily proceeded through a smoothing strategy. Moreover, to enhance the convergence, the trust-region constraint is introduced and the Tikhonov regularization is naturally called to tackle the constraint. Numerical examples are studied to verify the feasibility and efficiency of the proposed approach in breathing crack identification. [ABSTRACT FROM AUTHOR]

Water evaporation process is one of the main components of the hydrological cycle, according to which the correct estimation of this phenomenon plays an important role in irrigation management and river flow forecasting. Statistical and random models in the form of time series analysis are commonly used methods of estimation and forecasting. In this study, ARMA (autoregressive moving average), ARIMA (autoregressive integrated moving average), PARMA (periodic autoregressive moving average), and BL (bilinear) time series models (TSMs) are used to predict the annual and monthly pan evaporation values from the evaporation stations in several provinces of Iran in a 20-year statistical period. Results showed that PARMA model's accuracy in term of correlation coefficient and Nash–Sutcliffe efficiency for almost all 31 stations had a precise forecasting among other proposed TSMs. For PARMA model, the forecasting accuracy in term of NSE indicated that PARMA model almost was the promising model among other linear and nonlinear TSMs in prediction of Epan for all stations, except Arak (NSE = 0.94) and Qom (NSE = 0.93). The ARIMA model for Khorramabad and Bandar Abbas with NSE = 0.52 had the unreliable prediction for Epan compared with other stations. In addition, Arak station in term of RMSE had the least error, 23.79 mm/day and 10.90 mm/day, respectively, for training and testing stages among the other stations. [ABSTRACT FROM AUTHOR]

In this study, a modified two-time-scale model is proposed to overcome the limitations of the existing maneuvering analysis model. To this end, not only wave conditions but also all directions of ship operation velocities are considered in estimating wave drift force and moment. Subsequently, the increment of the drift force and moment induced by steady drift and yaw motion of a ship is imposed up to the first derivative of Taylor series expansion. By introducing this bilinear model, the burden of the drift force computation is reduced so that a more realistic and efficient seakeeping-maneuvering coupling analysis can be performed. A turning circle simulation in a regular short wave is carried out using the modified two-time-scale model. Then, the performance is validated by comparing its results with the direct coupling model. Moreover, quantitative improvement of the present numerical scheme and the influence of the operation velocities on ship maneuvering performance are discussed.

Many nonlinear models have been developed based on the mean errors modeling. However, the non-linear models with Autoregressive conditional heteoscedasticity are based on variance modeling. These models are combined with linear models, partly to increase the accuracy of modeling and predictions. In this study, using data from the Urmia Lake water level data for the period 1973-2012, the models with autocorrelation moving average and Bilinear model and two combined models (Autoregressive conditional heteoscedasticity) and (Bilinear conditional heteoscedasticity) were evaluated. To select the ARMA family models, AICC test were used and regression coefficient (r) and root mean square error (RMSE) tests were used for validation models. The results of validation the ARMA, BL, ARMA-ARCH and BL-ARCH models showed the correlation coefficient of 0.707, 0.618, 0.792 and 0.704 and the mean square root equal 2.838, 4.309, 2.031 and 4.11 between observed and modeling data respectively. Also the results showed that model accuracy increased with combining both linear and nonlinear models, but with combining two nonlinear models is caused reduce the accuracy of the models. Overall the results showed that by combining ARMA and ARCH models, the model error decreased about 28 percentage and combining two non-linear models caused increased model error about 2 percentage.

The paper presents new approach to estimation of the coefficients of an elementary bilinear time series model (EB). Until now, a lot of authors have considered different identifiability conditions for EB models which implicated different identifiability ranges for the model coefficient. However, all of these ranges have a common feature namely they are significantly narrower than the stability range of the EB model. This paper proposes a simple but efficient solution which makes an estimation of the EB model coefficient possible within its entire stability range.