Mohammad Gorji Sefidmazgi

A finite element based method for identification of switched linear systems

Non-stationary time series analysis is important in the study of complex systems. Finding mathematical models for such complex systems with transitions between different phases is an ill-posed problem. This paper brings the problem of time series analysis into the context of hybrid modeling. Approximating the hybrid system by a switched linear system, the problem is reduced to identifying the switching times and model parameters. To address this problem, the non-stationary time series clustering technique based on Finite Elements is used for modeling of switched linear systems. The advantage of this method is that it is not necessary to add restrictive statistical assumptions on system variables. Illustrative examples have been provided to verify the proposed algorithm.

Non-stationary Time Series Clustering with Application to Climate Systems

In climate science, knowledge about the system mostly relies on measured time series. A common problem of highest interest is the analysis of high-dimensional time series having different phases. Clustering in a multi-dimensional non-stationary time series is challenging since the problem is ill- posed. In this paper, the Finite Element Method of non-stationary clustering is applied to find regimes and the long-term trends in a temperature time series. One of the important attributes of this method is that it does not depend on any statistical assumption and therefore local stationarity of time series is not necessary. Results represent low-frequency variability of temperature and spatiotemporal pattern of climate change in an area despite higher frequency harmonics in time series.

Switched linear system identification based on bounded-switching clustering

This paper aims at identifying switched linear systems, which are described by noisy input/output data. This problem is originally non-convex and ill-posed. The proposed approach utilizes bounded-switching clustering method to convert the problem into a binary integer optimization and least square. This method optimally divides a time series into several clusters whose parameters are piecewise constant in time. Optimal number and order of linear sub-systems as well as the number of switches are selected using Akaike Information Criterion. The performance of the algorithm is evaluated through simulations. Parameters and structures of switched systems are found accurately in the presence of noise.

Time-series forecasting with evolvable partially connected artificial neural network

In nonlinear and chaotic time series prediction, constructing the mathematical model of the system dynamics is not an easy task. Partially connected Artificial Neural Network with Evolvable Topology (PANNET) is a new paradigm for prediction of chaotic time series without access to the dynamics and essential memory depth of the system. Evolvable topology of the PANNET provides flexibility in recognition of systems in contrast to fixed layered topology of the traditional ANNs. This evolvable topology guides the relationship between observation nodes and hidden nodes, where hidden nodes are extra nodes that play the role of memory or internal states of the system. In the proposed variable-length Genetic Algorithm (GA), internal neurons can be connected arbitrarily to any type of nodes. Besides, number of neurons, inputs and outputs for each neuron, origin and weight of each connection evolve in order to find the best configuration of the network.

Online Calibration of Inertial Sensors Using Kalman Filters and Artificial Neural Networks

Navigation is defined as finding the position of a moving vehicle and inertial navigation is among these methods. Unfortunately, inertial navigation has errors due to different reasons such as inertial sensors. These errors must be corrected by some means. In this paper, a method based on Kalman filters and artificial neural networks is introduced to calibrate inertial sensors during the navigation. Moreover, the proposed method provides better accuracy of the sensor models, when the navigation aid is not present for some times. Simulation results show the effectiveness of the proposed method as compared to the Kalman filter.

Delayed and Hidden Variables Interactions in Gene Regulatory Networks

Reverse Engineering of Gene Regulatory Networks (GRN), i.e. Finding appropriate mathematical models to understand complex cellular systems, can be used in disease diagnosis, treatment, and drug design. There are fundamental gaps in the construction of GRN with regard to modeling of hidden/delayed interactions. Addressing these deficiencies is critical to understanding complex intracellular processes and enabling full use of the vast and ever-growing amount of available genomic data. Current modeling strategies either ignore or oversimplify time delays resulted from transcription and translation processes during gene expression. In addition, many research works do not account hidden variables such as transcription factors, repressors, small metabolites, DNA, microRNA species that regulate themselves and other genes but are not readily detectable on micro array experiments. To capture the effect of these parameters, in this paper, we utilize our developed Partially Connected Artificial Neural Networks with Evolvable Topology (PANNET) to find a more comprehensive model of GRN by considering the effects of unknown hidden variables and different time delays. This method is innovative, since the structure of the network has memory and internal states, which can model the unknown hidden variables and time delays. We furthermore use a new evolutionary optimization based on variable-length Genetic Algorithm (GA) to find a sparse structure of PANNET to predict the gene expression levels accurately. Finally we demonstrate the capability of PANNET in constructing GRN, including the effect of different delays and unknown hidden variables through modeling of E. Coli SOS inducible DNA repair system.

Stable Gene Regulatory Network Modeling From Steady-State Data

Gene regulatory networks represent an abstract mapping of gene regulations in living cells. They aim to capture dependencies among molecular entities such as transcription factors, proteins and metabolites. In most applications, the regulatory network structure is unknown, and has to be reverse engineered from experimental data consisting of expression levels of the genes usually measured as messenger RNA concentrations in microarray experiments. Steady-state gene expression data are obtained from measurements of the variations in expression activity following the application of small perturbations to equilibrium states in genetic perturbation experiments. In this paper, the least absolute shrinkage and selection operator-vector autoregressive (LASSO-VAR) originally proposed for the analysis of economic time series data is adapted to include a stability constraint for the recovery of a sparse and stable regulatory network that describes data obtained from noisy perturbation experiments. The approach is applied to real experimental data obtained for the SOS pathway in Escherichia coli and the cell cycle pathway for yeast Saccharomyces cerevisiae. Significant features of this method are the ability to recover networks without inputting prior knowledge of the network topology, and the ability to be efficiently applied to large scale networks due to the convex nature of the method.

A Bilevel Parameter Tuning Strategy of Partially Connected ANNs

Partially connected ANN with Evolvable Topology (PANNET) is a non-fully connected recurrent neural network with proper number of context nodes. The structure of the network along with connection weights are determined through the evolutionary process of a customized genetic algorithm. In this paper, we develop an evolutionary bilevel optimization procedure for tuning the hyper-parameters of PANNET. In the upper level, an evolutionary algorithm optimizes the hyper-parameters, while the customized genetic algorithm is training the PANNET in the lower level optimization. Since executing the lower level optimization for each candidate hyper-parameters requires a high computational cost, fitness function approximation is performed using a regression model based on the Random Forest method. The proposed procedure provides more flexibility on choosing the hyper-parameters, and generate a smaller network with more accuracy in prediction.

Modeling Driver Behavior at Intersections with Takagi-Sugeno Fuzzy Models

Due to the relatively high density of vehicles and humans at intersections, it is crucial for an Advanced Driver Assistance System (ADAS) to predict human driver behaviors to avoid crashes. Due to the complexity of humans behavior interacting with a vehicle, it is very difficult to find an explicit model to analysis the drivers behavior. In this paper Takagi-Sugeno is used as a data driven technique to model and predict drivers behavior at intersections. In the proposed technique, a Takagi-Sugeno model is trained for each maneuver using a Gath-Geva clustering based algorithm. The proposed models are then evaluated with real time experimental data, and the estimation results are presented.

Identification of Switched Models in Non-Stationary Time Series based on Coordinate-Descent and Genetic Algorithm

Time series analysis is an important research topic in science and engineering. Real-world time series are usually non-stationary with time-varying parameters. Identification of non-stationary time series with a switched model includes finding the switch times and model parameters in each cluster. This problem is a non-convex optimization with equality constraints. Conventional identification methods suffer from restrictive statistical assumptions about the data or switch times, locality of solution, and computational complexity particularly for longer time series. In this paper, a novel coordinate-descent algorithm with the genetic algorithm (GA) and statistical inference is developed. In the evolutionary process, innovative types of crossover and mutation are proposed to improve exploration and exploitation capabilities of the GA, and fitness of the individuals are calculated by the maximum likelihood or least-mean-square.