Model Order Determination Research Articles

ARIMA-based Freight Forecasting and Network Optimization in E-commerce Logistics

Considering the proliferation of e-commerce platforms exemplified by Taobao and JD, the paradigm of online shopping has evolved into an integral facet of contemporary societal existence. To enhance network transport performance, it is essential to predict freight volume, assess existing capacity, and establish new sites to alleviate network pressure. This study focuses on a logistics transportation network, utilizing daily freight turnover data from January 1, 2021, to December 31, 2022. The ARIMA time series method is employed to forecast freight volumes at different sites within the e-commerce logistics network. Taking three logistics site route combinations, namely DC14→DC10, DC20→DC35, and DC25→DC62, as examples, two differencing operations are applied to meet the stationarity requirement of the ARIMA model. Autocorrelation and partial autocorrelation coefficients are used for preliminary model order determination. By minimizing the Akaike Information Criterion (AIC) value, an ARIMA (5) model is established. Single and multiple-step predictions are conducted, resulting in forecast curves for future freight volumes. Subsequently, an evaluation of the transportation network is performed, considering the importance of nodes and routes. The entropy weight method is applied to determine the weights of evaluation indicators. Importance indices for nodes and routes are calculated, leading to a ranking. For the assessment and selection of new site capabilities, Fisher's discriminant function is employed to classify different sites. The valuation level for site selection is determined, providing a scientific basis for the systematic choice of new sites.

Recursive Identification of Nonlinear Hammerstein Systems With FIR Linear Parts Under Impulsive Noise With Model Selection and Order Determination

Recursive Identification of Nonlinear Hammerstein Systems With FIR Linear Parts Under Impulsive Noise With Model Selection and Order Determination

Bayesian inference for order determination of double threshold variables autoregressive models

Abstract The reversible-jump Markov chain Monte Carlo (RJMCMC) algorithm can generate a jump Markov chain in the parameter space of different dimensions, and select a suitable model effectively. In this paper, when the order of the double threshold variables autoregressive (DT-AR) is unknown, the RJMCMC method is designed to identify the order of the DT-AR model in this paper. The simulation experiments and the real example show that the proposed method works well in identifying the order and estimating the parameters of the DT-AR model simultaneously.

Machine learning-based stochastic subspace identification method for structural modal parameters

Machine learning brings a new paradigm to the traditional structural modal parameter identification problem. In this study, we propose a novel machine learning method for stochastic subspace identification (SSI) problem. The proposed method embeds the mathematical characteristics of modal identification into a neural network and formalizes the modal identification into optimization problem of deep neural networks (DNN). The network optimization process is the process of obtaining modal parameters, which can be implemented in a relatively autonomous manner with little manual intervention. The designed modal identification network includes two sub-neural-networks: a model order determination neural network and modal identification neural network. In the model order determination neural network, the singular values of the Toeplitz matrix, which is constructed by output covariance matrices are fed into the network, and the designed network can automatically determine the model order by the designed loss function. In the modal identification neural network, the SSI principles are informed into the neural network, and the designed network is used to identify the modal parameters which optimizes the designed loss function to obtain the system matrix and output matrix. The examples of a numerical simulation and two actual bridges are used to illustrate the ability of the proposed method. Results show that the proposed method is capable of operating automatically to extract modal information from structural responses with stronger anti-interference ability and the identified number of accurate modes are obviously increased.

Correlation Coefficient‐Based Information Criterion for Quantification of Dependence Characteristics in Hydrological Time Series

AbstractQuantification of the dependence characteristics in hydrological time series is essential for understanding hydrological variability and for managing water resources. However, how determining a suitable model for describing the dependent components is still a challenge. In this article, we proposed a correlation coefficient‐based information criterion (CCIC) to determine the optimal model order of regression‐based models for quantifying the dependence characteristics in hydrological time series. CCIC was developed by combining the index of correlation coefficient and the information entropy index. The former was used to reflect the fitting error of the model and the latter was used as a penalty term to reflect the model uncertainty. They have similar roles as the two terms of the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) used commonly in hydrology. Results of Monte‐Carlo experiments verified higher and more stable accuracy of determining the true model order by CCIC than by AIC and BIC. Moreover, results indicated that the mean value of a time series had a big impact on the accuracy of CCIC. If the mean value of a time series was far from its initial value, the estimation of CCIC would have a big bias, causing low accuracy in the determination of suitable model order. The application of CCIC to annual precipitation from 520 stations in China further confirmed its advantages over AIC and BIC and indicated the significant short‐term dependence characteristics of annual precipitation in the Yangtze River basin. The proposed CCIC approach has potential for wider use in hydrometeorology.

Model Order Determination: A Multi-Objective Evolutionary Neural Network Scheme

Model Order Determination: A Multi-Objective Evolutionary Neural Network Scheme

Determination of the vocal tract model order in iterative adaptive inverse filtering

This paper is part of a special issue on Music Technology. Accurate estimation of glottal wave is an important method for singing voice analysis via voicing patterns. In this paper, an optimising method is proposed for automatic determination of vocal tract linear prediction analysis order that follows the specific situation of different voicing scenes based on Iterative Adaptive Inverse Filtering (IAIF) aiming at getting a more accurate glottal wave from speech or singing voice signal in a non-invasive way. In comparison with existing methods that use fixed experience order, the proposed method can achieve up to 8.41% improvement in correlation coefficient with the real glottal wave.

Structural Nonlinear Damage Identification Using the Residual Deviation Distance Conversion Index of the Time-Domain Model

Steel structures such as transmission towers may have cracks and other damages during the service period. When the structure vibrates, the cracks will open and close, which makes the structure have nonlinear characteristics of variant stiffness. In order to identify this type of nonlinear damage, a time-domain damage identification method based on the residual deviation distance (RDD) of the autoregressive conditional heteroskedasticity (ARCH) model is proposed. First, the basic theory of the ARCH model is introduced, and the methods of model order determination and parameter estimation are given. Then, the time-domain nonlinear damage characteristics are analyzed, and the second-order variance (SOV) index based on the ARCH model is introduced. Considering that both the ARCH model coefficient and the RDD contain nonlinear information, a conversion index is constructed using the Euclidean distance (ED) of the ARCH model coefficients before and after the damage. On this basis, an RDD conversion index is further proposed to improve the identification accuracy. Finally, a three-storey frame experiment and a complex transmission tower model experiment are used to verify the effectiveness of the proposed method. The experimental results show that the proposed RDD conversion index can better identify the location of structural damage, and the identification results of the RDD conversion index are obviously better than those of the SOV conversion index and the ED conversion index.

Research on Intelligent Analysis and Prediction Model of Funds Flow Based on Non-stationary Time Series

Funds flow prediction is critical to the stable operation of financial service institutions. In view of the non-stationary characteristics of funds inflow and outflow in financial institutions, this paper introduces the key characteristics of time series analysis, compares AR, MA, ARMA and ARIMA models, and proposes a funds flow prediction model based on ARIMA algorithm. The stationary test, pure randomness test and model order determination of time series are explained in detail. Finally, combined with the error and score of the model, the relatively optimal model is selected to predict the test data. The experimental results show that, for non-stationary time series, the model has smaller prediction error and can effectively predict funds flow.

The probabilistic tensor decomposition toolbox

This article introduces the probabilistic tensor decomposition toolbox - a MATLAB toolbox for tensor decomposition using Variational Bayesian inference and Gibbs sampling. An introduction and overview of probabilistic tensor decomposition and its connection with classical tensor decomposition methods based on maximum likelihood is provided. We subsequently describe the probabilistic tensor decomposition toolbox which encompasses the Canonical Polyadic, Tucker, and Tensor Train decomposition models. Currently, unconstrained, non-negative, orthogonal, and sparse factors are supported. Bayesian inference forms a principled way of incorporating prior knowledge, prediction of held-out data, and estimating posterior probabilities. Furthermore, it facilitates automatic model order determination, automatic regularization on factors (e.g. sparsity), and inherently penalizes model complexity which is beneficial when inferring hierarchical models, such as heteroscedastic noise modelling. The toolbox allows researchers to easily apply Bayesian tensor decomposition methods without the need to derive or implement these methods themselves. Furthermore, it serves as a reference implementation for comparing existing and new tensor decomposition methods. The software is available from https://github.com/JesperLH/prob-tensor-toolbox/.

Direct position determination and effective extraction of multiple transmitters

In this study, the problems, which simultaneously extract and direct positioning of multiple transmitters, are considered. Without assuming a priori knowledge of the source number, the multiple signal classification (MUSIC) algorithm is applied after using the Akaike information theoretic criteria for model order determination, while the minimum variance distortionless response (MVDR) algorithm can be directly used to localise multiple sources that transmit unknown signals. Two methods, which combine MUSIC and MVDR with the image expansion (IE) algorithm, are proposed. The IE algorithm used in actual scenarios is based on the constant-false-alarm rate. Simulation results show that the proposed algorithms can effectively extract and accurately localise multiple transmitters.

Simple Poisson PCA: an algorithm for (sparse) feature extraction with simultaneous dimension determination

Dimension reduction tools offer a popular approach to analysis of high-dimensional big data. In this paper, we propose an algorithm for sparse Principal Component Analysis for non-Gaussian data. Since our interest for the algorithm stems from applications in text data analysis we focus on the Poisson distribution which has been used extensively in analysing text data. In addition to sparsity our algorithm is able to effectively determine the desired number of principal components in the model (order determination). The good performance of our proposal is demonstrated with both synthetic and real data examples.

Estimating electromechanical oscillation modes from synchrophasor measurements in China Southern Power Grid

This paper proposes a generalized inverse and mode assurance criterion based stochastic subspace identification (GMSSI) method to improve the electromechanical mode estimation efficiency in China Southern Power Grid (CSG). Stochastic subspace identification (SSI) is first employed to estimate the state subspace model of power system from synchrophasor measurements. Then, a model order determination criterion is proposed to estimate the model order and the state matrix of power system is obtained. To accurately separate the electromechanical modes from trivial modes, the generalized inverse of SSI is used to estimate another state matrix. Further, the mode filtering and mode assurance criterion (MAC) are developed to distinguish the electromechanical modes. Simulation data and field-measurement data from CSG are used to evaluate the performance of the proposed GMSSI method. The comparison between existing measurement-based mode estimation methods and the proposed GMSSI demonstrates that the proposed GMSSI exhibits highly accurate, efficient and robust performance in estimating electromechanical modes from both ringdown and ambient data in bulk power grid.

Forecasting on first generation bioethanol production: A comparison of selected linear and non-linear models

Sustainable bioethanol production depends on the continuity of feedstock supply. Thus, an appropriate tool for feedstock supply forecasting is necessary for bioethanol production. This study was aimed at using forecasting models to predict feedstock supply and then estimating how much bioethanol could be produced from the forecasted bioethanol feedstocks as a major investigation in Turkey. It focused on running the linear model as Auto-Regressive (AR) and non-linear models as Auto-Regressive eXogeneous (ARX) and Auto-Regressive Moving Average eXogeneous (ARMAX) to forecast annual potential of wheat, corn, barley, and sugar beet which could be used as feedstock to produce first generation bioethanol. First, model order determination and modeling of feedstock production were studied for long prediction horizons. Model orders were estimated with major model order selection criteria: Akaike Information Criterion (AIC) and Final Prediction Error in the AR model. The same model orders were also used for the ARX model to compare, whereas model orders were determined based on the performance of the ARMAX model. Second, model performances were tested using Root Mean Square, R2, Chi-Square (χ2), and AIC for optimum model orders of each series. Finally, feedstock forecasts were determined to be quantitatively consistent for each model and with legal authority predictions. There were negligible small differences ranging from 0.8% to 2%. It is concluded that barley and wheat supplies have significant potential to produce bioethanol except for their primary use in food, seed, and feed consumption. However, sugar beet and corn are mainly used in Turkey.

Location identification of nonlinearities in MDOF systems through order determination of state-space models

This paper presents a new time-domain approach to identify locations of nonlinearities in multiple-degree-of-freedom (MDOF) systems. The approach is based on the well-known subspace method and utilizes the analysis of all the subsystems in the original MDOF system to determine locations of nonlinearities. The advantage of the proposed method is that it requires little prior knowledge about the system and does not need sampling under varying force amplitudes. Moreover, the method only needs the sampling of displacement data and thus avoids repetitive direct measurements or indirect numerical differentiation or integration to achieve velocity and acceleration data. In addition, benefitting from the subspace method, the approach is robust in noisy environment. However, one inconvenient drawback of the method is that it may misjudge linearity as nonlinearity under two specific circumstances. Several numerical simulations are carried out to test the performance of the approach, and the results demonstrate the consistency with the theoretical analysis.

Stochastic subspace identification‐based approach for tracking inter‐area oscillatory modes in bulk power system utilising synchrophasor measurements

Stochastic subspace identification (SSI) methods have been widely employed for oscillatory mode identification on probing and ambient data and are reported to have good performances. This work proposes a novel SSI-based approach for identifying dominant oscillatory mode from measurement data and extends the application of SSI to ringdown condition. The proposed approach first constructs an initial cluster of eigenvalues from SSI with repetitive calculations and then utilises a novel hierarchical clustering method to extract the dominant modes from the initial cluster. The repetitive calculations within the SSI are performed through varying the model order over a range defined by a novel initial order determination process. By doing so the challenge of model order determination for SSI-based methods is resolved. Moreover, benefiting from the repetitive calculations and the clustering process, the proposed approach is highly immune to prevalent noises in the measurements. Finally, the proposed approach is applied and validated on the field-measurement data from the phasor measurement units of China Southern Power Grid (CSG) through comparisons with Prony, ARMAX, and Monte Carlo methods. Test results demonstrate that the proposed approach performs with high accuracy, robustness, and efficiency in CSG.

A Radial Basis Function Algorithm with Automatic Model Order Determination

We present a new radial basis function (RBF) algorithm for constructing nonlinear models from data that may be sparsely scattered in high dimensions. We propose a simplified method for identifying function locations that is based on an approximation to the autocorrelation function. Local regions are now defined based on zero crossings of the modified autocorrelation contribution. The resulting local spatiotemporal data appear to capture increased structure as evidenced by the reduced number of basis functions required to achieve algorithm convergence and the fact that the resulting approximations have significantly improved accuracy. We prove a zero crossing lemma and convergence of the algorithm in the norm for continuous functions over a compact domain. Further, we show that several hypotheses tests can be used to detect this convergence. The model parameters and the number of basis functions are determined automatically from the given data. The only user parameter is the confidence level of the hypotheses tests which we fix at 95% . We apply the algorithm to modeling data on manifolds and the prediction of a chaotic time series using compactly supported skew RBFs in the setting of the overdetermined data fitting problem.

A systematic state-of-charge estimation framework for multi-cell battery pack in electric vehicles using bias correction technique

In order to maximize the capacity/energy utilization and guarantee safe and reliable operation of battery packs used in electric vehicles, an accurate cell state-of-charge (SoC) estimator is an essential part. This paper tries to add three contributions to the existing literature. (1) An integrated battery system identification method for model order determination and parameter identification is proposed. In addition to being able to identify the model parameters, it can also locate an optimal balance between model complexity and prediction precision. (2) A radial basis function (RBF) neural network based uncertainty quantification algorithm has been proposed for constructing response surface approximate model (RSAM) of model bias function. Based on the RSAM, the average pack model can be applied to every single cell in battery pack and realize accurate terminal voltage prediction. (3) A systematic SoC estimation framework for multi-cell series-connected battery pack of electric vehicles using bias correction technique has been proposed. Finally, three cases with twelve lithium-ion polymer battery (LiPB) cells series-connected battery pack are used to verify and evaluate the proposed framework. The result indicates that with the proposed systematic estimation framework the maximum absolute SoC estimation error of all cells in the battery pack are less than 2%.

Non-informative hierarchical Bayesian inference for non-negative matrix factorization

Non-negative matrix factorization (NMF) is an intuitive, non-negative, and interpretable approximation method. Canonical NMF approach could derive some basic components to represent original data, while probabilistic NMF approaches try to introduce some reasonable constraints to optimize the canonical NMF model. However, both of them cannot handle ground-truth bases discovering and model order determination problems. In general, the model order of basis matrix needs to be pre-defined. The model order determines the capability and accuracy of data structure discovering. However, how to accurately infer the model order of basis matrix has not been well investigated. In this paper, we propose a method called non-informative hierarchical Bayesian non-negative matrix factorization (NHBNMF) to automatically determine the model order and discover the data structure. They are achieved through hierarchical Bayesian inference model, maximum a posteriori (MAP) criterion, and non-informative parameters. In NHBNMF method, we first introduce a structure with two-level parameters to enable the entire model to approach the distributions of ground-truth bases. Then we use non-informative parameter scheme to eliminate the hyper-parameter to enable automatic searching. Finally, the model order and ground-truth bases are discovered by using MAP criterion and L2-norm selection. The experiments are conducted based on both synthetic and real-world datasets to show the effectiveness of our algorithm. The results demonstrate that our algorithm can accurately estimate the model order and discover the ground-truth bases. Even for the complicated FERET facial dataset, our algorithm still obtained interpretable bases and achieved satisfactory accuracy of the model order estimation.

On applicability of PCA, voxel-wise variance normalization and dimensionality assumptions for sliding temporal window sICA in resting-state fMRI

Subject-level resting-state fMRI (RS-fMRI) spatial independent component analysis (sICA) may provide new ways to analyze the data when performed in the sliding time window. However, whether principal component analysis (PCA) and voxel-wise variance normalization (VN) are applicable pre-processing procedures in the sliding-window context, as they are for regular sICA, has not been addressed so far. Also model order selection requires further studies concerning sliding-window sICA. In this paper we have addressed these concerns. First, we compared PCA-retained subspaces concerning overlapping parts of consecutive temporal windows to answer whether in-window PCA and VN can confound comparisons between sICA analyses in consecutive windows. Second, we compared the PCA subspaces between windowed and full data to assess expected comparability between windowed and full-data sICA results. Third, temporal evolution of dimensionality estimates in RS-fMRI data sets was monitored to identify potential challenges in model order selection in a sliding-window sICA context. Our results illustrate that in-window VN can be safely used, in-window PCA is applicable with most window widths and that comparisons between windowed and full data should not be performed from a subspace similarity point of view. In addition, our studies on dimensionality estimates demonstrated that there are sustained, periodic and very case-specific changes in signal-to-noise ratio within RS-fMRI data sets. Consequently, dimensionality estimation is needed for well-founded model order determination in the sliding-window case. The observed periodic changes correspond to a frequency band of ≤0.1 Hz, which is commonly associated with brain activity in RS-fMRI and become on average most pronounced at window widths of 80 and 60 time points (144 and 108 s, respectively). Wider windows provided only slightly better comparability between consecutive windows, and 60 time point or shorter windows also provided the best comparability with full-data results. Further studies are needed to determine the cause for dimensionality variations.