Adaptive computation algorithm for RBF neural network

Data-Driven Intelligent Warning Method for Membrane Fouling

Membrane fouling has become a serious issue in membrane bioreactor (MBR) and may destroy the operation of the wastewater treatment process (WWTP). The goal of this article is to design a data-driven intelligent warning method for warning the future events of membrane fouling in MBR. The main novelties of the proposed method are threefold. First, a soft-computing model, based on the recurrent fuzzy neural network (RFNN), was proposed to identify the real-time values of membrane permeability. Second, a multistep prediction strategy was designed to predict the multiple outputs of membrane permeability accurately by decreasing the error accumulation over the predictive horizon. Third, a warning detection algorithm, using the state comprehensive evaluation (SCE) method, was developed to evaluate the pollution levels of MBR. Finally, the proposed method was inserted into a warning system to complete the predicting and warning missions and further tested in the real plants to evaluate its efficiency and effectiveness. Experimental results have verified the benefits of the proposed method.

RBFNN-Based Data-Driven Predictive Iterative Learning Control for Nonaffine Nonlinear Systems

In this paper, a novel data-driven predictive iterative learning control (DDPILC) scheme based on a radial basis function neural network (RBFNN) is proposed for a class of repeatable nonaffine nonlinear discrete-time systems subjected to nonrepetitive external disturbances. First, by utilizing the dynamic linearization technique (DLT) with a newly introduced and unknown system parameter pseudopartial derivative (PPD) and designing a new RBFNN estimation algorithm along the iterative learning axis for addressing the unknown PPD and the unknown nonrepetitive external disturbances, a data-driven prediction model is established. It is theoretically shown that by constructing a composite energy function (CEF) with respect to the modeling error for the first time, the convergence of the modeling error via the proposed DLT-based RBFNN modeling method can be guaranteed, and the convergence speed is tunable. Then, a DDPILC with a disturbance compensation term is designed, and the convergence of the tracking control error is analyzed. Finally, simulations of a train operation system reveal that even if the train suffers from randomly varying load disturbances and nonlinear running resistance, the proposed scheme can make both the modeling error and the tracking control error decrease successively with increasing operation number.

Applications of machine learning for simulations of red blood cells in microfluidic devices

Background

For optimization of microfluidic devices for the analysis of blood samples, it is useful to simulate blood cells as elastic objects in flow of blood plasma. In such numerical models, we primarily need to take into consideration the movement and behavior of the dominant component of the blood, the red blood cells. This can be done quite precisely in small channels and within a short timeframe. However, larger volumes or timescales require different approaches. Instead of simplifying the simulation, we use a neural network to predict the movement of the red blood cells.

Results

The neural network uses data from the numerical simulation for learning, however, the simulation needs only be run once. Alternatively, the data could come from video processing of a recording of a biological experiment. Afterwards, the network is able to predict the movement of the red blood cells because it is a system of bases that gives an approximate cell velocity at each point of the simulation channel as a linear combination of bases.In a simple box geometry, the neural network gives results comparable to predictions using fluid streamlines, however in a channel with obstacles forming slits, the neural network is about five times more accurate.The network can also be used as a discriminator between different situations. We observe about two-fold increase in mean relative error when a network trained on one geometry is used to predict trajectories in a modified geometry. Even larger increase was observed when it was used to predict trajectories of cells with different elastic properties.

Conclusions

While for uncomplicated box channels there is no advantage in using a system of bases instead of a simple prediction using fluid streamlines, in a more complicated geometry, the neural network is significantly more accurate. Another application of this system of bases is using it as a comparison tool for different modeled situations. This has a significant future potential when applied to processing data from videos of microfluidic flows.

Optimized Structure of the Traffic Flow Forecasting Model With a Deep Learning Approach

Forecasting accuracy is an important issue for successful intelligent traffic management, especially in the domain of traffic efficiency and congestion reduction. The dawning of the big data era brings opportunities to greatly improve prediction accuracy. In this paper, we propose a novel model, stacked autoencoder Levenberg-Marquardt model, which is a type of deep architecture of neural network approach aiming to improve forecasting accuracy. The proposed model is designed using the Taguchi method to develop an optimized structure and to learn traffic flow features through layer-by-layer feature granulation with a greedy layerwise unsupervised learning algorithm. It is applied to real-world data collected from the M6 freeway in the U.K. and is compared with three existing traffic predictors. To the best of our knowledge, this is the first time that an optimized structure of the traffic flow forecasting model with a deep learning approach is presented. The evaluation results demonstrate that the proposed model with an optimized structure has superior performance in traffic flow forecasting.

Neural Approximation-Based Adaptive Control for a Class of Nonlinear Nonstrict Feedback Discrete-Time Systems

In this paper, an adaptive control approach-based neural approximation is developed for a class of uncertain nonlinear discrete-time (DT) systems. The main characteristic of the considered systems is that they can be viewed as a class of multi-input multioutput systems in the nonstrict feedback structure. The similar control problem of this class of systems has been addressed in the past, but it focused on the continuous-time systems. Due to the complicacies of the system structure, it will become more difficult for the controller design and the stability analysis. To stabilize this class of systems, a new recursive procedure is developed, and the effect caused by the noncausal problem in the nonstrict feedback DT structure can be solved using a semirecurrent neural approximation. Based on the Lyapunov difference approach, it is proved that all the signals of the closed-loop system are semiglobal, ultimately uniformly bounded, and a good tracking performance can be guaranteed. The feasibility of the proposed controllers can be validated by setting a simulation example.

Efficient least angle regression for identification of linear-in-the-parameters models

Least angle regression, as a promising model selection method, differentiates itself from conventional stepwise and stagewise methods, in that it is neither too greedy nor too slow. It is closely related to L₁ norm optimization, which has the advantage of low prediction variance through sacrificing part of model bias property in order to enhance model generalization capability. In this paper, we propose an efficient least angle regression algorithm for model selection for a large class of linear-in-the-parameters models with the purpose of accelerating the model selection process. The entire algorithm works completely in a recursive manner, where the correlations between model terms and residuals, the evolving directions and other pertinent variables are derived explicitly and updated successively at every subset selection step. The model coefficients are only computed when the algorithm finishes. The direct involvement of matrix inversions is thereby relieved. A detailed computational complexity analysis indicates that the proposed algorithm possesses significant computational efficiency, compared with the original approach where the well-known efficient Cholesky decomposition is involved in solving least angle regression. Three artificial and real-world examples are employed to demonstrate the effectiveness, efficiency and numerical stability of the proposed algorithm.

Neural Network Control-Based Adaptive Learning Design for Nonlinear Systems With Full-State Constraints

In order to stabilize a class of uncertain nonlinear strict-feedback systems with full-state constraints, an adaptive neural network control method is investigated in this paper. The state constraints are frequently emerged in the real-life plants and how to avoid the violation of state constraints is an important task. By introducing a barrier Lyapunov function (BLF) to every step in a backstepping procedure, a novel adaptive backstepping design is well developed to ensure that the full-state constraints are not violated. At the same time, one remarkable feature is that the minimal learning parameters are employed in BLF backstepping design. By making use of Lyapunov analysis, we can prove that all the signals in the closed-loop system are semiglobal uniformly ultimately bounded and the output is well driven to follow the desired output. Finally, a simulation is given to verify the effectiveness of the method.

A Unified Approach to Adaptive Neural Control for Nonlinear Discrete-Time Systems With Nonlinear Dead-Zone Input

In this paper, an effective adaptive control approach is constructed to stabilize a class of nonlinear discrete-time systems, which contain unknown functions, unknown dead-zone input, and unknown control direction. Different from linear dead zone, the dead zone, in this paper, is a kind of nonlinear dead zone. To overcome the noncausal problem, which leads to the control scheme infeasible, the systems can be transformed into a m -step-ahead predictor. Due to nonlinear dead-zone appearance, the transformed predictor still contains the nonaffine function. In addition, it is assumed that the gain function of dead-zone input and the control direction are unknown. These conditions bring about the difficulties and the complicacy in the controller design. Thus, the implicit function theorem is applied to deal with nonaffine dead-zone appearance, the problem caused by the unknown control direction can be resolved through applying the discrete Nussbaum gain, and the neural networks are used to approximate the unknown function. Based on the Lyapunov theory, all the signals of the resulting closed-loop system are proved to be semiglobal uniformly ultimately bounded. Moreover, the tracking error is proved to be regulated to a small neighborhood around zero. The feasibility of the proposed approach is demonstrated by a simulation example.

A direct self-constructing neural controller design for a class of nonlinear systems

This paper is concerned with the problem of adaptive neural control for a class of uncertain or ill-defined nonaffine nonlinear systems. Using a self-organizing radial basis function neural network (RBFNN), a direct self-constructing neural controller (DSNC) is designed so that unknown nonlinearities can be approximated and the closed-loop system is stable. The key features of the proposed DSNC design scheme can be summarized as follows. First, different from the existing results in literature, a self-organizing RBFNN with adaptive threshold is constructed online for DSNC to improve the control performance. Second, the control law and adaptive law for the weights of RBFNN are established so that the closed-loop system is stable in the term of Lyapunov stability theory. Third, the tracking error is guaranteed to uniformly asymptotically converge to zero with the aid of an additional robustifying control term. An example is finally given to demonstrate the design procedure and the performance of the proposed method. Simulation results reveal the effectiveness of the proposed method.

Adaptive NN controller design for a class of nonlinear MIMO discrete-time systems

An adaptive neural network tracking control is studied for a class of multiple-input multiple-output (MIMO) nonlinear systems. The studied systems are in discrete-time form and the discretized dead-zone inputs are considered. In addition, the studied MIMO systems are composed of N subsystems, and each subsystem contains unknown functions and external disturbance. Due to the complicated framework of the discrete-time systems, the existence of the dead zone and the noncausal problem in discrete-time, it brings about difficulties for controlling such a class of systems. To overcome the noncausal problem, by defining the coordinate transformations, the studied systems are transformed into a special form, which is suitable for the backstepping design. The radial basis functions NNs are utilized to approximate the unknown functions of the systems. The adaptation laws and the controllers are designed based on the transformed systems. By using the Lyapunov method, it is proved that the closed-loop system is stable in the sense that the semiglobally uniformly ultimately bounded of all the signals and the tracking errors converge to a bounded compact set. The simulation examples and the comparisons with previous approaches are provided to illustrate the effectiveness of the proposed control algorithm.

Modeling of batch processes using explicitly time-dependent artificial neural networks

A neural network architecture incorporating time dependency explicitly, proposed recently, for modeling nonlinear nonstationary dynamic systems is further developed in this paper, and three alternate configurations are proposed to represent the dynamics of batch chemical processes. The first configuration consists of L subnets, each having M inputs representing the past samples of process inputs and output; each subnet has a hidden layer with polynomial activation function; the outputs of the hidden layer are combined and acted upon by an explicitly time-dependent modulation function. The outputs of all the subnets are summed to obtain the output prediction. In the second configuration, additional weights are incorporated to obtain a more generalized model. In the third configuration, the subnets are eliminated by incorporating an additional hidden layer consisting of L nodes. Backpropagation learning algorithm is formulated for each of the proposed neural network configuration to determine the weights, the polynomial coefficients, and the modulation function parameters. The modeling capability of the proposed neural network configuration is evaluated by employing it to represent the dynamics of a batch reactor in which a consecutive reaction takes place. The results show that all the three time-varying neural networks configurations are able to represent the batch reactor dynamics accurately, and it is found that the third configuration is exhibiting comparable or better performance over the other two configurations while requiring much smaller number of parameters. The modeling ability of the third configuration is further validated by applying to modeling a semibatch polymerization reactor challenge problem. This paper illustrates that the proposed approach can be applied to represent dynamics of any batch/semibatch process.

Data-driven MFAC for a class of discrete-time nonlinear systems with RBFNN

A novel model-free adaptive control method is proposed for a class of discrete-time single input single output (SISO) nonlinear systems, where the equivalent dynamic linearization technique is used on the ideal nonlinear controller. With radial basis function neural network, the controller parameters are tuned on-line directly using the measured input and output data of the plant, when the plant model is unavailable. The stability of the proposed method is guaranteed by rigorous theoretical analysis, and the effectiveness and applicability are verified by numerical simulation and further demonstrated by the experiment on three tanks water level control process.

Nonlinear systems modeling based on self-organizing fuzzy-neural-network with adaptive computation algorithm

In this paper, a self-organizing fuzzy-neural-network with adaptive computation algorithm (SOFNN-ACA) is proposed for modeling a class of nonlinear systems. This SOFNN-ACA is constructed online via simultaneous structure and parameter learning processes. In structure learning, a set of fuzzy rules can be self-designed using an information-theoretic methodology. The fuzzy rules with high spiking intensities (SI) are divided into new ones. And the fuzzy rules with a small relative mutual information (RMI) value will be pruned in order to simplify the FNN structure. In parameter learning, the consequent part parameters are learned through the use of an ACA that incorporates an adaptive learning rate strategy into the learning process to accelerate the convergence speed. Then, the convergence of SOFNN-ACA is analyzed. Finally, the proposed SOFNN-ACA is used to model nonlinear systems. The modeling results demonstrate that this proposed SOFNN-ACA can model nonlinear systems effectively.

RBF-based technique for statistical demodulation of pathological tremor

This paper presents an innovative technique based on the joint approximation capabilities of radial basis function (RBF) networks and the estimation capability of the multivariate iterated Hilbert transform (IHT) for the statistical demodulation of pathological tremor from electromyography (EMG) signals in patients with Parkinson's disease. We define a stochastic model of the multichannel high-density surface EMG by means of the RBF networks applied to the reconstruction of the stochastic process (characterizing the disease) modeled by the multivariate relationships generated by the Karhunen-Loéve transform in Hilbert spaces. Next, we perform a demodulation of the entire random field by means of the estimation capability of the multivariate IHT in a statistical setting. The proposed method is applied to both simulated signals and data recorded from three Parkinsonian patients and the results show that the amplitude modulation components of the tremor oscillation can be estimated with signal-to-noise ratio close to 30 dB with root-mean-square error for the estimates of the tremor instantaneous frequency. Additionally, the comparisons with a large number of techniques based on all the combinations of the RBF, extreme learning machine, backpropagation, support vector machine used in the first step of the algorithm; and IHT, empirical mode decomposition, multiband energy separation algorithm, periodic algebraic separation and energy demodulation used in the second step of the algorithm, clearly show the effectiveness of our technique. These results show that the proposed approach is a potential useful tool for advanced neurorehabilitation technologies that aim at tremor characterization and suppression.

Real-time model predictive control using a self-organizing neural network

In this paper, a real-time model predictive control (RT-MPC) based on self-organizing radial basis function neural network (SORBFNN) is proposed for nonlinear systems. This RT-MPC has its simplicity in parallelism to model predictive control design and efficiency to deal with computational complexity. First, a SORBFNN with concurrent structure and parameter learning is developed as the predictive model of the nonlinear systems. The model performance can be significantly improved through SORBFNN, and the modeling error is uniformly ultimately bounded. Second, a fast gradient method (GM) is enhanced for the solution of optimal control problem. This proposed GM can reduce computational cost and suboptimize the RT-MPC online. Then, the conditions of the stability analysis and steady-state performance of the closed-loop systems are presented. Finally, numerical simulations reveal that the proposed control gives satisfactory tracking and disturbance rejection performances. Experimental results demonstrate its effectiveness.

Decirculation process in neural network dynamics

We describe a decirculation process which marks perturbations of network structure and neural updating that are necessary for evolutionary neural networks to proceed from one circulating state to another. Two aspects of control parameters, screen updating and flow diagrams, are developed to quantify such perturbations, and hence to manage the dynamics of evolutionary neural networks. A dynamic state-shifting algorithm is derived from the decirculation process. This algorithm is used to build models of evolutionary content-addressable memory (ECAM) networks endowed with many dynamic relaxation processes. By the training of ECAM networks based on the dynamic state-shifting algorithm, we obtain the classification of training samples and the construction of recognition mappings, both of which perform adaptive computations essential to CAM.