Game-theoretic decision making has the potential to bring human-like reasoning skills to autonomous vehicles (AVs), fostering trust between humans and AVs. However, to make these approaches sufficiently practical for real-world use, challenges such as game complexity and incomplete information have to be addressed. Game complexity refers to the difficulties in solving a game-theoretic problem, which include solution existence, algorithm convergence, and scalability. We show in our recent work that a possible solution to overcoming these difficulties is to use potential games. However, constructing a potential game often requires specific cost function designs, limiting their broad use. To address this challenge, we propose to employ a game projection technique in this paper, relaxing the cost function design conditions and making the potential game approach applicable to broader scenarios, even including the ones that cannot be modelled as a potential game. Incomplete information refers to the ego vehicle’s lack of knowledge of other traffic agents’ cost functions. In a driving scenario, deviations of the ego vehicle assumed/estimated others’ cost functions from their actual ones are often inevitable. This necessitate the robustness analysis of a game-theoretic solution. This paper defines the robustness margin of a game solution as the maximum magnitude of cost function deviations that can be accommodated without changing the optimality of the game solution. With this definition, closed-form robustness margins are derived. Numerical studies using highway lane-changing scenarios are reported.

Autoencoders have been extensively used in the development of recent anomaly detection techniques. The premise of their application is based on the notion that after training the autoencoder on normal training data, anomalous inputs will exhibit a significant reconstruction error. Consequently, this enables a clear differentiation between normal and anomalous samples. In practice, however, it is observed that autoencoders can generalize beyond the normal class and achieve a small reconstruction error on some of the anomalous samples. To improve the performance, various techniques propose additional components and more sophisticated training procedures. In this work, we propose a remarkably straightforward alternative: instead of adding neural network components, involved computations, and cumbersome training, we complement the reconstruction loss with a computationally light term that regulates the norm of representations in the latent space. The simplicity of our approach minimizes the requirement for hyperparameter tuning and customization for new applications which, paired with its permissive data modality constraint, enhances the potential for successful adoption across a broad range of applications. We test the method on various visual and tabular benchmarks and demonstrate that the technique matches and frequently outperforms more complex alternatives. We further demonstrate that implementing this idea in the context of state-of-the-art methods can further improve their performance. We also provide a theoretical analysis and numerical simulations that help demonstrate the underlying process that unfolds during training and how it helps with anomaly detection. This mitigates the black-box nature of autoencoder-based anomaly detection algorithms and offers an avenue for further investigation of advantages, fail cases, and potential new directions.

Black-box artificial intelligence (AI) induction methods such as deep reinforcement learning (DRL) are increasingly being used to find optimal policies for a given control task. Although policies represented using a black-box AI are capable of efficiently executing the underlying control task and achieving optimal closed-loop performance-controlling the agent from the initial time step until the successful termination of an episode, the developed control rules are often complex and neither interpretable nor explainable. In this article, we use a recently proposed nonlinear decision-tree (NLDT) approach to find a hierarchical set of control rules in an attempt to maximize the open-loop performance for approximating and explaining the pretrained black-box DRL (oracle) agent using the labeled state-action dataset. Recent advances in nonlinear optimization approaches using evolutionary computation facilitate finding a hierarchical set of nonlinear control rules as a function of state variables using a computationally fast bilevel optimization procedure at each node of the proposed NLDT. In addition, we propose a reoptimization procedure for enhancing the closed-loop performance of an already derived NLDT. We evaluate our proposed methodologies (open- and closed-loop NLDTs) on different control problems having multiple discrete actions. In all these problems, our proposed approach is able to find relatively simple and interpretable rules involving one to four nonlinear terms per rule, while simultaneously achieving on par closed-loop performance when compared to a trained black-box DRL agent. A postprocessing approach for simplifying the NLDT is also suggested. The obtained results are inspiring as they suggest the replacement of complicated black-box DRL policies involving thousands of parameters (making them noninterpretable) with relatively simple interpretable policies. The results are encouraging and motivating to pursue further applications of proposed approach in solving more complex control tasks.

Engine calibration problems are black-box optimization problems which are evaluation costly and most of them are constrained in the objective space. In these problems, decision variables may have different impacts on objectives and constraints, which could be detected by sensitivity analysis. Most existing surrogate-assisted evolutionary algorithms do not analyze variable sensitivity, thus, useless effort may be made on some less sensitive variables. This article proposes a surrogate-assisted bilevel evolutionary algorithm to solve a real-world engine calibration problem. Principal component analysis is performed to investigate the impact of variables on constraints and to divide decision variables into lower-level and upper-level variables. The lower-level aims at optimizing lower-level variables to make candidate solutions feasible, and the upper-level focuses on adjusting upper-level variables to optimize the objective. In addition, an ordinal-regression-based surrogate is adapted to estimate the ordinal landscape of solution feasibility. Computational studies on a gasoline engine model demonstrate that our algorithm is efficient in constraint handling and also achieves a smaller fuel consumption value than other state-of-the-art calibration methods.

A Stackelberg differential game theoretic model predictive controller is proposed for an autonomous highway driving problem. The hierarchical controller’s high-level component is the two-player Stackelberg differential lane change game, where each player uses a model predictive controller (MPC) to control his/her own motion. The differential game is converted into a bi-level optimization problem and is solved with the branch and bound algorithm. Additionally, an inverse MPC algorithm is developed to estimate the weights of the MPC cost function of the target vehicle. The low-level hybrid MPC controls both the autonomous vehicle’s longitudinal motion and its real-time lane determination. Simulations indicate both the inverse MPC’s capability on aggressiveness estimation of target vehicles and DGTMPC’s superior performance in interactive lane change situations.

The paper proposes a novel hierarchical recurrent neural network architecture for on-line classification and interpretation of EEG data. It incorporates two dynamic pools of neurons - one based on NeuCube three dimensional structure of spiking neurons, spatially mapping a brain template and connected via spike-timing dependent plastic synapses and another Echo state neural network (ESN) reservoir of sparsely connected hyperbolic tangent neurons that is able to learn on-line to classify continuously extracted from the Cube spike-rate features. The aim of the work was to interpret and classify in a brain-inspired manner dynamic spatio-temporal brain signals. The achieved results demonstrate improved classification accuracy on a benchmark EEG data set along with a good interpretability of the data. In future, the proposed method can be used for classification of other brain spatio-temporal data, such as ECOG and fMRI.

Decision-making for autonomous driving is challenging, considering the complex interactions among multiple traffic agents (including autonomous vehicles (AVs), human-driven vehicles, and pedestrians) and the computational load needed to evaluate these interactions. This paper develops two general potential game-based frameworks, namely, finite and continuous potential games, for decision-making in autonomous driving. The two frameworks account for the AVs’ two types of action spaces, i.e., finite and continuous action spaces, respectively. The developed frameworks provide theoretical guarantees for the existence of pure-strategy Nash equilibria and for the convergence of the Nash equilibrium (NE) seeking algorithms. The scalability challenge is also addressed. In addition, we provide cost function shaping approaches such that the agents’ cost functions not only reflect common driving objectives but also yield potential games. The performance of the developed algorithms is demonstrated in diverse traffic scenarios, including intersection-crossing and lane-changing scenarios. Statistical comparative studies, including 1) finite potential game vs. continuous potential game, 2) best response dynamics vs. potential function optimization, and 3) potential game vs. reinforcement learning (RL) vs. control barrier function (CBF), are conducted to compare the robustness against various surrounding vehicles’ strategies and to compare the computational efficiency. It is shown that the developed potential game frameworks have better robustness than RL and than CBF if the surrounding vehicles are not safety-conscious, and are computationally feasible for real-time implementation.

Meta Reinforcement Learning (Meta-RL) has seen substantial advancements recently. In particular, off-policy methods were developed to improve the data efficiency of Meta-RL techniques. Probabilistic embeddings for actor-critic$\boldsymbol{RL}$(PEARL) is a leading approach for multi-MDP adaptation problems. A major drawback of many existing Meta-RL methods, including PEARL, is that they do not explicitly consider the safety of the prior policy when it is exposed to a new task for the first time. Safety is essential for many real world applications, including field robots and Autonomous Vehicles (AVs), In this paper, we develop the PEARL PLUS (PEARL+) algorithm, which optimizes the policy for both prior (pre-adaptation) safety and posterior (after-adaptation) performance. Building on top of PEARL, our proposed PEARL+algorithm introduces a prior regularization term in the reward function and a new Q-network for recovering the state-action value under prior context assumptions, to improve the robustness to task distribution shift and safety of the trained network exposed to a new task for the first time. The performance of PEARL+is validated by solving three safety-critical problems related to robots and AVs, including two MuJoCo benchmark problems. From the simulation experiments, we show that safety of the prior policy is significantly improved and more robust to task distribution shift compared to PEARL.

In this paper, a three-level decision-making framework is developed to generate safe and effective decisions for autonomous vehicles (AVs). A key component in this decision framework is a normal-form game to capture the interactions between the ego vehicle and its surrounding vehicles. The payoffs in the normal-form game are designed to capture both safety reward and the reward gained by obeying (or the price paid by violating) “soft” traffic rules, e.g., first-come-first-go. This game formulation enables the ego to 1) make appropriate decisions considering the payoffs and possible actions of its surrounding vehicles, and 2) take intelligent actions in emergencies that may sacrifice some soft traffic rules to ensure safety. Moreover, we introduce parameters in the payoff matrix to tune the ego vehicle’s behavior, e.g., aggressiveness level. A neural network is developed to learn the tuning parameters via supervised learning. In addition, to enable the ego to respond timely to different surrounding vehicles’ driving styles, driving style characterization is incorporated into the payoff design for the normal-form game. Simulation studies are conducted to demonstrate the performance of the developed algorithms in two-vehicle intersection-crossing and lane-changing scenarios.

An online evolving method, named evolving finite state machine (e-FSM), is proposed to develop an optimal Markov driving model. The model has the same properties as a standard Markov model, but its states and transition dynamics evolve without human supervision. In this article, we introduce: 1) the principles of the e-FSM’s novel capabilities:online state determinationandonline transition-dynamics identificationfor elaborating the Markov driving model and 2) an advanced online evolving framework (a-OEF) for supporting the reinforcement-learning-based controller’s decision making by using the evolved model. For the evaluation of the proposed methodology and framework, the ego vehicle is controlled by the double deep${Q}$-network (DDQN) controller with and without the a-OEF in the multilane driving scenario where various naturalistic traffic situations are simulated. Simulation results show that better control performance in terms offastandsafedriving is achieved via the DDQN with the a-OEF, which demonstrates that the Markov driving models evolved by the e-FSMs effectively support detecting and revising the controller’s incorrect decision making.

This article describes a novel approach to the problem of developing explainable machine learning models. We consider a deep reinforcement learning (DRL) model representing a highway path planning policy for autonomous highway driving [1]. The model constitutes a mapping from the continuous multidimensional state space characterizing vehicle positions and velocities to a discrete set of actions in longitudinal and lateral direction. It is obtained by applying a customized version of the double deep Q-network learning algorithm [2]. The main idea is to approximate the DRL model with a set of IF-THEN rules that provide an alternative interpretable model, which is further enhanced by visualizing the rules. This concept is rationalized by the universal approximation properties of the rule-based models with fuzzy predicates. The proposed approach includes a learning engine composed of zero-order fuzzy rules, which generalize locally around the prototypes by using multivariate function models. The adjacent (in the data space) prototypes, which correspond to the same action, are further grouped and merged into the so-called MegaClouds reducing significantly the number of fuzzy rules. The input selection method is based on ranking the density of the individual inputs. Experimental results show that the specific DRL agent can be interpreted by approximating with families of rules of different granularity. The method is computationally efficient and can be potentially extended to addressing the explainability of the broader set of fully connected deep neural network models.

In future mobility environment, virtual drivers of autonomous vehicles should be monitored for the sake of safety by evaluating their driving behaviors. Evaluating human drivers of non-autonomous vehicles also can be helpful to improve performance of safety control systems. This paper evaluates driving behaviors based on transition probabilities among multiple driving modes. We estimate transition probabilities with likelihoods of multiple modes from an interacting multiple model by proposing an online estimation approach. The proposed approach addresses the numerical issue found in our preliminary work, and it is verified with an extensive simulation. Furthermore, we evaluate driving behaviors by utilizing the estimated transition probabilities. The proposed method of driving behavior evaluation is demonstrated experimentally.

This article provides an overview of fuzzy encoded Markov chains (FEMCs), which are finite-state Markov chains applied to transitions between fuzzy sets that encode signal or variable values. FEMCs can be used for modeling of dynamic systems, predicting/forecasting future signal values, for state estimation, and for the development of fuzzy rules for control. Under suitable assumptions, the state possibility distribution can be propagated using FEMC models in a similar manner as the state probability distribution using conventional Markov chain models. The article first discusses FEMC theory, procedures to identify FEMCs from data, and the use of FEMCs for forecasting and control. Then, we introduce, for the first time, observers for partially observable FEMCs. The observer theory is developed and computational approaches are presented. Finally, we briefly review some FEMC applications in the automotive domain.

To commemorate the 50th anniversary of the IEEE Transactions on Systems, Man, and Cybernetics: Systems, this article examines and reports on its past to current topical coverage of systems science and engineering toward exploring the evolving focus of the research community. Results of a systematic bibliometric analysis are presented with associated conclusions, implications, and summary of topical areas. In addition, respective views regarding the current state of the field and where it is headed are offered by recent leaders of the IEEE Systems, Man, and Cybernetics Society, including its continued relevance and role in the advancement of systems technology.

In this paper, we present a safe deep reinforcement learning system for automated driving. The proposed framework leverages merits of both rule-based and learning-based approaches for safety assurance. Our safety system consists of two modules namely handcrafted safety and dynamically-learned safety. The handcrafted safety module is a heuristic safety rule based on common driving practice that ensure a minimum relative gap to a traffic vehicle. On the other hand, the dynamically-learned safety module is a data-driven safety rule that learns safety patterns from driving data. Specifically, the dynamically-leaned safety module incorporates a model lookahead beyond the immediate reward of reinforcement learning to predict safety longer into the future. If one of the future states leads to a near-miss or collision, then a negative reward will be assigned to the reward function to avoid collision and accelerate the learning process. We demonstrate the capability of the proposed framework in a simulation environment with varying traffic density. Our results show the superior capabilities of the policy enhanced with dynamically-learned safety module.

This paper addresses the trajectory planning problem for autonomous vehicles in traffic. We build a stochastic Markov decision process (MDP) model to represent the behaviors of the vehicles. This MDP model takes into account the road geometry and is able to reproduce more diverse driving styles. We introduce a new concept, namely, the “dynamic cell,” to dynamically modify the state of the traffic according to different vehicle velocities, driver intents (signals), and the sizes of the surrounding vehicles (i.e., truck, sedan, and so on). We then use Bézier curves to plan smooth paths for lane switching. The maximum curvature of the path is enforced via certain design parameters. By designing suitable reward functions, different desired driving styles of the intelligent vehicle can be achieved by solving a reinforcement learning problem. The desired driving behaviors (i.e., autonomous highway overtaking) are demonstrated with an in-house developed traffic simulator.

This paper presents a real-time-capable recursive fuzzy learning algorithm (FLA) for learning transition probabilities in Markov Chain (MC) from observed information and its performance on speed prediction. In detail, real-time state transition is observed at each step as the latest information to update the MC. Accordingly FLA locates a parallelogram area in the MC state transition table in a fuzzy way. Cells in this area are updated with different weights such that transition probabilities of the transitions more similar to the observed one receive a bigger increase while those of less similar transitions get a smaller increase. Numeric examples are given to illustrate FLA’s learning pattern, its good prediction capability of vehicle speed and its low computation cost, comparing to normal MC, constant velocity model, constant acceleration model, autoregressive model with exogenous input and back-propagation neural networks.

In many industrial applications, one of the major bottlenecks in using advanced learning-based methods (such as reinforcement learning) for controls is the lack of interpretability of the trained agent. In this paper, we present a methodology for translating a trained reinforcement learning agent into a set of simple and easy to interpret if-then rules by using the proven universal approximation property of the rules with fuzzy predicates. Proposed methodology combines the optimality of reinforcement learning with interpretability of the theory of approximate reasoning, thus making reinforcement learning-based solutions more accessible to industrial practitioners. The framework presented in this paper has the potential to help address the fundamental problem in widespread adoption of reinforcement learning in industrial applications.

This paper describes a new self-organizing neuro-fuzzy approach to autonomously learn interpretable models by self-driving cars. A new explainable self-organizing architecture and a new density-based feature selection method are proposed. These new approaches are used to classify different action states occurring from different self-driving conditions. The proposed approach is able to provide human understandable IF ... THEN rules representation due to its learning engine which is composed of a massively parallel set of 0-order fuzzy rules. The proposed density-based feature selection method is based on the ranking of the densities of each feature in the data space, and takes advantage of the parallel characteristic of the proposed explainable self-organizing approach to create individualized subsets of features per class. The main goal of both proposed methods is to provide highly accurate models with high transparency, interpretability, and explainability for self-driving vehicles. In order to validate our proposal, experiments were realized using a real dataset provided by Ford Motor Company. The dataset contains different driving states occurring during self-driving performances. Results demonstrate that the proposed approach could surpass its state-of-the-art competitors in terms of accuracy for this challenge multiclass classification problem.

Objective: Individuals with paralysis often have mobility and dexterity impairments that limit their ability to operate motor vehicle controls. Integrating brain-machine interface (BMI) neurotechnology with vehicle control systems (VCS) provides a novel solution to this problem. In this proof-of-concept study, we show that an intracortical BMI developed to restore voluntary grasp can be repurposed to decode motor intention for vehicle velocity and steering control. Methods: The BMI-VCS consists of four components: 1) implanted motor cortex microelectrode array and NeuroPort data acquisition system, 2) machine learning workstation, 3) Python interface to generate control signals, and 4) vehicle control system. Results: Direct cortical steering and velocity control were achieved through accurate decoding of movement intention (supination, pronation, hand open, hand close) from the participant's motor cortex, translating intention into vehicle commands (turn right, turn left, accelerate, decelerate, respectively), and dynamically switching between commands to turn corners, start and stop, shift from forward to reverse, and parallel park. Conclusion: By translating BMI decoder outputs into high-level vehicle commands, a participant with tetraparesis from C5 ASIA A spinal cord injury successfully navigated CARLA driving simulator courses in real time. These decoder outputs could also be used offline for shared control of a scale model car. Significance: High-level, shared vehicle control with BMI-VCS offers an innovative way to return independent driving abilities to those with disability. BMI systems that can control multiple end-effectors may be particularly useful to those with paralysis.

The operational space of an autonomous vehicle (AV) can be diverse and vary significantly. Due to this, formulating a rule based decision maker for selecting driving maneuvers may not be ideal. Similarly, it may not be efficient to solve optimal control problem in real-time for a predefined cost function. In order to address these issues and to avoid peculiar behaviors when encountering unforeseen scenario, we propose a reinforcement learning (RL) based method, where the ego car, i.e., an autonomous vehicle, learns to make decisions by directly interacting with the simulated traffic. Here the decision maker is a deep neural network that provides an action choice for a given system state. We demonstrate the performance of the developed algorithm in highway driving scenario where the trained AV encounters varying traffic density.

Performance of vehicle control systems, such as active safety systems and driver assistance systems, can be significantly improved by taking driver behavior information into consideration. This paper implements a handling limit-based algorithm for driver behavior characterization by introducing stochastic perspective with the interacting multiple model (IMM) estimation theory. The proposed algorithm constructs mathematical models for four vehicle dynamics categories. The IMM estimator is designed for each vehicle dynamics category to evaluate driver scores. The proposed algorithm is compared with an existing handling limit-based algorithm through experimental tests, and the results illustrate advantages of the proposed algorithm.

Given a route to a destination, a mobile robot still needs to locally plan a path to avoid collisions in continuously changing environment, e.g., a hall with pedestrians and moving obstacles. In this paper, diffusion maps are applied to find a local path for reaching a goal and avoiding collisions simultaneously. The proposed path planning algorithm plans a local path by utilizing a receding horizon approach, and therefore the algorithm repeats planning at every sample time. With this approach, mobile robots do not have to carry a prior map all the time because updated environment information is used for planning at every sample time. Extensive simulation is performed in different scenarios and demonstrates a good performance in collision avoidance.

This paper studies the decision making problem of autonomous vehicles in traffic. We model the interaction between an autonomous vehicle and the environment as a stochastic Markov decision process (MDP) and consider the driving style of an experienced driver as the target to be learned. The road geometry is taken into consideration in the MDP model in order to incorporate more diverse driving styles. By designing the reward function of the MDP, the desired, driving behavior of the autonomous vehicle is obtained using reinforcement learning. Simulated results demonstrate the desired driving behaviors of an autonomous vehicle.

Inspired by the idealism embodied in Russell and Whitehead’s “Principia Mathematica,” Wiener marched along a different and unique path toward sciences of intelligence and behavior which culminated at “Cybernetics: Or Control and Communication in the Animal and the Machine” 70 years ago. Since then, we have witnessed the birth of Cognitive Science, Artificial Intelligence (AI), Computational Intelligence, and many other new research fields and disciplines, all of which have been catalyzed by Cybernetics. The IEEE Systems, Man, AND Cybernetics Society and this Transactions on Cybernetics have become the focal point of the broad cybernetics community by promoting the theory, practice, and interdisciplinary aspects of systems science and engineering, human-machine systems, and cybernetics principles. It is a time of celebration and reflection.

Vehicle speed prediction can benefit a wide range of vehicle control designs, especially for fuel economy applications. This paper shows a computationally light vehicle short term speed predictor designed for on-board implementation, using minimal information of speed measurement only. The predictor generalizes historical speed data's underlying pattern and predicts from probability aspect. One novelty of the method is the usage of fuzzy modeling to eliminate the resolution limitation in vehicle acceleration state definition, classification, and prediction. The method uses Auto-regressive (AR) model to capture vehicle speed data's short term dynamics, and classifies the data into multiple acceleration states by fuzzy membership. In the prediction process, acceleration measurements are mapped to the Markov states by fuzzy encoding, and future acceleration states are predicted by Markov transition. Deterministic speed prediction is calculated from the trained AR models, which are selected by fuzzy state membership similarity. The developed predictor is tested with a vehicle's real urban driving data, and the effectiveness of the incorporated techniques is verified by a comparison study.

Evaluating driving performance of autonomous vehicles is as important as developing automated driving algorithms. In order to ensure passenger safety, evaluation of driving behavior is required before delivering autonomous vehicles to customers. An Interacting Multiple Model (IMM)-based driver evaluation algorithm was developed and it provides various information associated with multiple driving aggressiveness modes. This paper estimates transition probabilities by utilizing those information from the IMM-based evaluation algorithm, which are expected to unveil hidden driving performance of autonomous vehicles. Three estimation approaches are presented and they are tested with experimental drives.

We explore the use of adaptive control for a hydraulic actuator model in an engine with variable cam timing (VCT) system. The hydraulic actuator is modeled as a Hammer-stein system with an asymmetric, uncertain input nonlinearity followed by known time delay and linear dynamics. We begin the presentation by designing a fixed-gain baseline controller, which consists of a PI controller with high robustness margins, followed by a nonlinear-inverse lookup-table(LUT) controller. This baseline controller is shown to result in poor closed-loop performance in the presence of mismatch between the nonlinear-inverse controller and the input nonlinearity due to uncertainty. We formulate a recursive least-squares adaptation scheme that is applicable to piecewise-linear MISO LUTs, and apply the adaptation scheme to update the entries of the nonlinear-inverse LUT controller to handle the uncertainty in the nonlinearity. The adaptive system delivers superior closed-loop performance compared to the baseline architecture by self-tuning the nonlinear-inverse controller to the actual input nonlinearity.

This paper investigates a comfort-based route planner that considers both travel time and ride comfort. We first present a framework of simultaneous road profile estimation and anomaly detection with commonly available vehicle sensors. A jump-diffusion process-based state estimator is developed and used along with a multi-input observer for road profile estimation. The estimation framework is evaluated in an experimental test vehicle and promising performance is demonstrated. Second, three objective comfort metrics are developed based on factors such as travel time, road roughness, road anomaly, and intersection. A comfort-based route planning problem is then formulated with these metrics and an extended Dijkstra's algorithm is exploited to solve the problem. A cloud-based implementation of our comfort-based route planning approach is proposed to facilitate information access and fast computation. Finally, a real-world case study, comfort-based route planning from Ford Research and Innovation Center, Michigan to Ford Rouge Factory Tour, Michigan, is presented to illustrate the efficacy of the proposed route planning framework.

This paper considers a new clustering algorithm for processing time-evolving road anomaly reports. Two cluster categories, main and outlier, are defined to deal with outliers as well as to capture the evolving nature of road anomalies. The Mahalanobis distance is exploited to quantify the similarity between a new report and the existing clusters. The clusters are maintained online and the Woodbury matrix inverse lemma is used for their recursive updates. The proposed clustering algorithm can localize isolated anomalies and compress information for densely distributed anomalies. A simulation is presented to demonstrate the efficacy of the proposed algorithm.

Incorporating driver behavior information into vehicle control strategies can significantly improve performance of vehicle control systems, such as active safety systems and driver assistance systems. This paper proposes an algorithm for driver behavior characterization based on handling limits. In order to implement the handling limit-based algorithm, an interacting multiple model estimation technique is applied, which accounts for probabilistic correctness of the multiple models. The proposed algorithm is validated through experimental tests, and the results illustrate potential of the proposed algorithm as a stochastic approach for driver behavior characterization based on handling limits.

A general memetic trajectory optimization method is introduced. The method is comprised of an evolutionary algorithm (EA) for global optimization, followed by local optimization. The global optimization algorithm is biogeography-based optimization (BBO), which is an EA motivated by the migratory behavior of biological organisms. For local optimization, we start with identifying a local linearized model within the region of the BBO solution by approximating the linear model with Jacobian matrix, and then optimize trajectory using gradient method. The process iterates Jacobian learning and optimization until an optimal trajectory is identified. We apply this memetic algorithm to a time-to-torque minimization problem for a gasoline turbocharged direct injection automotive engine. The optimized trajectory demonstrates significant improvement over the intuitive bang-bang controls that were originally thought to deliver the fastest transient torque response. Simulation results show that BBO decreases time-to-torque by 48% relative to bang-bang controls, and adaptive optimization decreases time-to-torque by an additional 26%. These results have significant implications for improved automotive engine performance.

This paper presents a safety-based route planner that exploits vehicle-to-cloud-to-vehicle (V2C2V) connectivity. Time and road risk index (RRI) are considered as metrics to be balanced based on user preference. To evaluate road segment risk, a road and accident database from the highway safety information system is mined with a hybrid neural network model to predict RRI. Real-time factors such as time of day, day of the week, and weather are included as correction factors to the static RRI prediction. With real-time RRI and expected travel time, route planning is formulated as a multiobjective network flow problem and further reduced to a mixed-integer programming problem. A V2C2V implementation of our safety-based route planning approach is proposed to facilitate access to real-time information and computing resources. A real-world case study, route planning through the city of Columbus, Ohio, is presented. Several scenarios illustrate how the "best" route can be adjusted to favor time versus safety metrics.

The previous studies have shown that optimizing the driving velocity profiles and route selection based on the availability of the traffic lights' operation information in a traffic network can significantly reduce the individual and cumulative energy consumption of on-road vehicles for the urban driving. In this paper, we propose an accurate and precise stochastic online estimation method of the parameters of the traffic lights operating at a piecewise constant period. In this paper, we first model the traffic lights with a semi-hidden Markov model (SHMM) and then develop the period measurement model governed by a unique noise model specific to the indirect traffic light period measurements. The proposed method solves the estimation problem in two stages: in the first stage, we determine the sequence of the Markovian states maximizing the probability given the measurements and the SHMM parameters; then, in the second stage, we update the period and state duration estimates based on the Bayesian tracking given the corresponding latest measurements. The simulation and real vehicle data results prove that the proposed method can accurately estimate the switching times and the period of the piecewise fixed-period traffic lights.

Advanced driver assistance systems, such as unintentional lane departure warning systems, have recently drawn much attention and R & D efforts. Such a system may assist the driver by monitoring the driver or vehicle behaviors to predict/detect driving situations (e.g., lane departure) and alert the driver to take corrective action. In this paper, we show how the support vector machine (SVM) methodology can potentially provide enhanced unintentional lane departure prediction, which is a new method relative to literature. Our binary SVM employed the Radial Basis Function kernel to classify time series of select vehicle variables. The SVM was trained and tested using the driver experiment data generated by VIRTTEX, a hydraulically powered 6-degrees-of-freedom moving base driving simulator at Ford Motor Company. The data that we used represented 16 drowsy subjects (three-hour driving time per subject) and six control subjects (20 minutes driving per subject), all of which drove a simulated 2000 Volvo S80. The vehicle variables were all sampled at 50 Hz. There were a total of 3,508 unintentional lane departure occurrences for the drowsy drivers and only 23 for four of the six control drivers (two had none). The SVM was trained by over 60,000 time series examples (the actual number depended on the prediction horizon) created from 50% of the lane departures. The training data were removed from the testing data. During the testing, the SVM made a lane departure prediction at every sampling time for every one of the 22 drivers (over 6.8 million predictions in total). The overall sensitivity and specificity of the SVM with a 0.2-second prediction horizon for the 22 drivers were 99.77465% and 99.99997%, respectively. The SVM predicted, on average 0.200181 seconds in advance, lane departure correctly for all the control drivers, but missed 4 of the 1,758 and gave false positives for another 2 for the drowsy drivers. For the prediction horizon of 0.4s, there was 1 false positive case for the control subjects, and the false negative and false positive cases rose substantially to 10 and 137 for the drowsy drivers, respectively.

The three-way catalytic converter performance degrades as it ages over time due to many phenomenon such as catalyst poisoning, sintering or physical damage of the instrument. To reduce the emission impact on environment, the Environmental Protection Agency (EPA) regulations requires the on-board diagnostics (OBD) method to set a flag (fault code) once the catalyst reaches its threshold. In this work, we propose a support vector machine based non-intrusive classification method to diagnose the catalyst as it ages. To further improve the model robustness and to reduce the size of support vectors, multiple clustering algorithms were evaluated. The model was tested on multiple catalyst systems under various operating conditions and good results were observed.

This paper proposes a novel multi-objective route planning approach within the framework of a Vehicle-to-Cloud-to-Vehicle (V2C2V) architecture. Time and road risk index (RRI) are both considered as metrics. To evaluate road segment risk, an accident database from the Highway Safety Information System (HSIS) is processed to build a comprehensive road risk assessment model. Route planning is formulated as a multi-objective network flow problem and further reduced to a Mixed Integer Programming (MIP) problem. A real-world case study, route planning through the city of Columbus, Ohio, is presented. The Vehicle-to-Cloud-to-Vehicle (V2C2V) based implementation of our safety-based route planning approach is proposed to facilitate access to real-time information and computing resources.

This paper presents a modeling framework based on finite-state space Markov chains (MCs) and fuzzy subsets to represent signals that vary in a continuous range. Our special attention to this extension of finite-state space MC modeling is motivated by numerous opportunities in applying MC models to represent physical variables in automotive and aerospace systems and, subsequently, using these models for fault detection, estimation, prediction, stochastic dynamic programming, and stochastic model predictive control. Our generalized MC modeling framework synergistically combines the notion of transition probabilities with information granulation based on fuzzy partitioning. As compared with the case of more familiar interval partitioning, the transition probabilities in our model are defined for transitions between fuzzy subsets rather than intervals/rectangular cells. Our framework is first introduced for scalar-valued signals and then extended to vector-valued signals. A real-time capable recursive algorithm for learning transition probabilities from measured signal data is derived. Formulas that characterize the possibility distribution of the next signal value and predict the next signal value are given. It is shown that the introduced modeling framework based on MC models defined over fuzzy partitioning inherits all properties and represents a natural extension of MC models defined over interval partitioning, while providing interpolation ability and improved prediction accuracy. In addition, we derive an alternative formulation of the Chapman–Kolmogorov equation that applies to models in possibilistic/fuzzy environment. Examples are given to illustrate the key notions and results based on modeling of the vehicle speed and road grade signals.

Driving style, road geometry, and traffic conditions have a significant impact on vehicles' fuel economy. In general, drivers are not aware of the optimal velocity profile for a given route. Indeed, the global optimal velocity trajectory depends on many factors, and its calculation requires intensive computations. In this paper, we discuss the optimization of the speed trajectory to minimize fuel consumption and communicate it to the driver. With this information the driver can adjust his/her speed profile to reduce the overall fuel consumption. We propose to perform the computation-intensive calculations on a distinct computing platform called the “cloud.” In our approach, the driver sends the information of the intended travel destination to the cloud. In the cloud, the server generates a route, collects the associated traffic and geographical information, and solves the optimization problem by a spatial domain dynamic programming (DP) algorithm that utilizes accurate vehicle and fuel consumption models to determine the optimal speed trajectory along the route. Then, the server sends the speed trajectory to the vehicle where it is communicated to the driver. We tested the approach on a prototype vehicle equipped with a visual interface mounted on the dash of a test vehicle. The test results show 5%-15% improvement in fuel economy depending on the driver and route without a significant effect on the travel time. Although this paper implements the speed advisory system in a conventional vehicle, the solution is generic, and it is applicable to any kind of powertrain structure.

Feedback error learning is an on-line learning strategy of inverse dynamics. It sequentially acquires an inverse model of a plant through feedback control actions. The inverse model is usually implemented as a Neural Network, however we propose a new approach to implement the FEL control scheme through Piecewise Bilinear models. We present an on-line sequential learning algorithm for feedforward controller design. We also propose an algorithm for off-line identification of a pseudo-inverse model of a plant to use as an initial feedforward controller before its learning. We will prove the applicability of PB models to implement the FEL scheme through illustrative examples.

This paper addresses modeling and predicting vehicle fuel economy based on simple vehicle characteristics. The models are identified using a historical vehicle fuel economy data set. First, the use of least squares regression analysis is pursued, and a mathematical model is created that is capable of predicting highway fuel economy based on six vehicle characteristics: engine displacement volume, vehicle maximum power, vehicle maximum torque, vehicle weight, vehicle wheelbase, and vehicle cross sectional area. Then neural network models are developed and shown to achieve higher accuracy as compared to the regression models, with 70 percent of the data in the validation data set predicted within 2 mpg. Furthermore, we demonstrate that by employing a hybrid architecture, where vehicles are first clustered and then separate models are developed for vehicle clusters, the model accuracy can be improved further.

This paper studies characterizing the driving behavior during steady-state and transient car-following. An approach utilizing the online learning of an evolving Takagi-Sugeno fuzzy model that is combined with a probabilistic model is applied to capture the multi-model and evolving nature of the driving behavior. The approach is validated by testing on a vehicle during different driving conditions.

This paper deals with a new class of Markov Chain type models that can be effectively used for real time modeling and on-line learning of nonlinear systems with uncertainties. We expand the concept of the generalized Markov Chain - a probabilistic model that synergistically combines the idea of transition probabilities with the information granulation paradigm. We consider generalized Markov chains based on two different types of information granules - intervals and fuzzy subsets - and the methods for their learning from data. We also analyze the relationship between the Markov chains and the fuzzy models and derive an alternative formulation of the Chapman-Kolmogorov equation that applies to stochastic models in fuzzy environment. As this approach is motivated by and intended for in-vehicle applications, results are illustrated on examples of granular models of vehicle speed and road grade.

Advanced vehicle cabin technologies provide drivers infotainment, navigation, and enhanced convenient driving experiences. As interaction between the driver and in cabin technologies increases it is beneficial to provide tailored driver communication for an improved cabin experience. Assessment of the driving demand is of particular value to assist in modulating communication and vehicle system interactions with the driver. The complex vehicle, driver, and environment driving contexts require innovative prognostic approaches to driver workload inference. This paper presents a Hybrid Intelligent System for Driver Workload Estimation (HWLE). The real-time HWLE soft computing modules incorporate expert models, model-driven reasoning, and specialized computational intelligence techniques to compute an aggregated WLE-Index. The context depended WLE-Index facilitates tailoring vehicle-driver communication and interaction based on the driving demand. Results from application of the HWLE system under real-time conditions are presented.

This paper presents a practical framework for autonomous monitoring of industrial equipment based on novelty detection. It overcomes limitations of current equipment monitoring technology by developing a “generic” structure that is relatively independent of the type of physical equipment under consideration. The kernel of the proposed approach is an “evolving” model based on unsupervised learning methods (reducing the need for human intervention). The framework employs procedures designed to temporally evolve the critical model parameters with experience for enhanced monitoring accuracy (a critical ability for mass deployment of the technology on a variety of equipment/hardware without needing extensive initial tune-up). Proposed approach makes explicit provision to characterize the distinct operating modes of the equipment, when necessary, and provides the ability to predict both abrupt as well as gradually developing (incipient) changes. The framework is realized as an autonomous software agent that continuously updates its decision model implementing an unsupervised recursive learning algorithm. Results of validation of the proposed methodology by accelerated testing experiments are also discussed.

This paper studies to characterize driver driving behavior or driver control structure in real time. The three proposed methods use some of the signals such as the driver actuation measurements, the relative ranges between a leading and a following vehicle during a car-following maneuver, and the vehicle dynamic responses such as the vehicle's longitudinal acceleration and deceleration. All the used signals exist in various electronic control systems. Vehicle tests were conducted on a test vehicle to illustrate the effectiveness of the proposed methods in identifying aggressive and cautious driving behaviors.

It is a well-recognized fact that the theory of fuzzy sets and systems, for the last four decades after the seminal paper by Professor Zadeh [1], has demonstrated its remarkable ability to go beyond conventional information representation. It resulted in a wide range of new formulations of practical problems, such as fuzzy control, fuzzy clustering and classification, fuzzy modeling, and fuzzy optimization [2]. Historically, the design of the fuzzy systems has been initially assumed to be centered on expert knowledge [3]. During the 1990s, a new trend emerged [4], [5] that offered techniques to make use of the experimental data. This data-centered approach can be used to enhance and validate the existing expert knowledge or can also be used to substitute its lack (as is the case with autonomous systems, for example). Neurofuzzy and hybrid learning systems were introduced, where fuzzy representation was integrated into a neural learning architecture to bring linguistic meaning of the learned information [5]. (c) IEEE Press

In this paper the recently introduced evolving fuzzy classifier method called eClass is studied in respect to its architecture and evolution of the fuzzy rule-base. The proposed classifier has an open/evolving structure and can start 'from scratch', learning and adapting to the new data samples. Alternatively, if an initial fuzzy rule-based classifier, generated beforehand in off-line mode or provided by the operator, exists then eClass can evolve this initial classifier in on-line mode. In other words, the fuzzy rule base will evolve incorporating new rules, modifying and/or, possibly, removing some of the previously existing ones. Additionally, the parameters of both, the antecedent and the consequent parts are adapted. Note that eClass can start with an empty rule-base, which is a unique feature of this approach. The proposed approach is free from user-specified parameters and the mechanism of forming new rules is very robust. In this paper, four different modelling architectures are described and compared. The architectures are based on (i) unsupervised cluster partitions, eClassC; (ii) Sugeno fuzzy models with singleton consequents, eClassA; (iii) Takagi-Sugeno fuzzy models with linear consequent functions, eClassB; and (iv) a multi-model classification architecture, where separate TS regression models are combined to form an overall classification output of the system, eClassM. A thorough comparison of the results when applying each of these architectures and the results using previously existing classifiers has been made using an online interactive self-adaptive image classification framework.

Resistance spot welding is one of the primary means of joining sheet metal in the automotive industry and other industries. The demand for improved corrosion resistance has led the automotive industry to increasingly use zinc coated steel in auto body construction. One of the major concerns associated with welding coated steel is the mushrooming effect (the increase in the electrode diameter due to deposition of copper into the spot surface) resulting in reduced current density and undersized welds (cold welds). The most common approach to this problem is based on the use of simple unconditional incremental algorithms (steppers) for preprogrammed current scheduling. In this paper, an intelligent algorithm is proposed for adjusting the amount of current to compensate for the electrodes degradation. The algorithm works as a fuzzy logic controller using a set of engineering rules with fuzzy predicates that dynamically adapt the secondary current to the state of the weld process. The state is identified by indirectly estimating two of the main process characteristics - weld quality and expulsion rate. A soft sensor for indirect estimation of the weld quality employing a learning vector quantization (LVQ) type classifier is designed to provide a real time approximate assessment of the weld nugget diameter. Another soft sensing algorithm is applied to predict the impact of changes in current on the expulsion rate of the weld process. By maintaining the expulsion rate just below a minimal acceptable level, robust process control performance and satisfactory weld quality are achieved. The intelligent constant current control for resistance spot welding is implemented and validated on a medium frequency direct current (MFDC) constant current weld controller. Results demonstrate a substantial improvement of weld quality and reduction of process variability due to the proposed new control algorithm.

This paper presents an innovative on-line approach for autonomous diagnostics and prognostics. It overcomes limitations of current diagnostics and prognostics technology by developing a "generic" framework that is relatively independent of the type of physical equipment under consideration. Proposed diagnostics and prognostics framework (DPF) is based on unsupervised learning methods (reducing the need for human intervention). The procedures used in DPF are designed to temporally evolve the critical parameters with monitoring experience for enhanced diagnostic/prognostic accuracy (a critical ability for mass deployment of the technology on a variety of equipment/ hardware without needing extensive initial tune-up). This framework is currently under deployment in a major automotive manufacturing plant in Michigan, USA. Results from this pilot program to date are very satisfactory.

This paper deals with a simplified version of the evolving Takagi-Sugeno (eTS) learning algorithm - a computationally efficient procedure for on-line learning TS type fuzzy models. It combines the concept of the scatter as a measure of data density and summarization ability of the TS rules, the use of Cauchy type antecedent membership functions, an aging indicator characterizing the stationarity of the rules, and a recursive least square algorithm to dynamically learn the structure and parameters of the eTS model

Article Share on Intelligent agent for automated manufacturing rule generation Authors: Alan Clark Ford Motor Company Ford Motor CompanyView Profile , Dimitar Filev Ford Motor Company Ford Motor CompanyView Profile Authors Info & Claims CIKM '04: Proceedings of the thirteenth ACM international conference on Information and knowledge managementNovember 2004Pages 495–500https://doi.org/10.1145/1031171.1031266Published:13 November 2004Publication History 3citation491DownloadsMetricsTotal Citations3Total Downloads491Last 12 Months2Last 6 weeks0 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteGet Access

Evolving Takagi-Sugeno (eTS) fuzzy models and the method for their on-line identification has been recently introduced as an effective tool for design of flexible system models with minimum a priori information. Their structure develops on-line during the process of model identification itself. In this paper, this approach has been extended for the case of multi-input multi-output (MIMO) system model. Both parts of the identification algorithm, namely the unsupervised fuzzy rule-base antecedents learning by a recursive, noniterative clustering, and the supervised linear sub-model parameters learning by Kalman-filtering-based procedure, are extended for the MIMO case. The radius of influence of each fuzzy rule is considered a vector instead of a scalar as in the original eTS approach, allowing different areas of the data space to be covered by each input variable. As in the eTS, in MIMO eTS, the rule-base and parameters of the fuzzy model continually evolve by adding new rules with more summarization power and by modifying existing rules and parameters. Simulation results using a well-known benchmark are considered in this paper. Further investigation concern the application of MIMO eTS to predictive modeling of the speech spectrum magnitude, classification of multi-channel source modulation etc.

This paper links the well-known technique of statistical process control (SPC) monitoring to the concept of rule-based fuzzy modeling. A family of if ... then rules with fuzzy predicates describes the set of steady state input-output relationships when the process variations are due to process noise (common causes). The ability of the SPC method to on-line diagnose a change in the distribution of the process variables is used to identify a new operating point of the systems, and consequently the initiation of a new potential rule. The model is applied as a decision support tool to help identify the optimal changes of the inputs associated with the special causes and to minimize the time for their elimination. A case study on automotive paint process optimization that is based on this concept is presented.

A flexible model in the form of an artificial neural network (NN) with evolving structure (eNN) is represented in the paper in the form of the evolving fuzzy Takagi-Sugeno model. It falls into the same category of models as the recently introduced evolving rule-based (eR) models. The learning algorithm is incremental, unsupervised and is based on the on-line identification of Takagi-Sugeno type quasilinear models. Both eR and eNN differ from the other model schemes by their gradually evolving structure as opposed to the fixed structure models, in which only parameters are subject to optimization or adaptation. Essentially, it represents a Takagi-Sugeno model with gradually evolving set of rules, determined on-line. This approach has potential in both modeling and control using indirect learning mechanisms. Its computational efficiency is based on the non-iterative and recursive procedure, which combines a Kalman filter with proper initializations, and online unsupervised clustering. eNN has been tested with data from a real air-conditioning installation. Applications to real-time adaptive non-linear control, fault detection and diagnostics, performance analysis, time-series forecasting, knowledge extraction and accumulation, etc. are possible directions of their use in the future research.

An approach to the online learning of Takagi-Sugeno (TS) type models is proposed in the paper. It is based on a novel learning algorithm that recursively updates TS model structure and parameters by combining supervised and unsupervised learning. The rule-base and parameters of the TS model continually evolve by adding new rules with more summarization power and by modifying existing rules and parameters. In this way, the rule-base structure is inherited and up-dated when new data become available. By applying this learning concept to the TS model we arrive at a new type adaptive model called the Evolving Takagi-Sugeno model (ETS). The adaptive nature of these evolving TS models in combination with the highly transparent and compact form of fuzzy rules makes them a promising candidate for online modeling and control of complex processes, competitive to neural networks. The approach has been tested on data from an air-conditioning installation serving a real building. The results illustrate the viability and efficiency of the approach. The proposed concept, however, has significantly wider implications in a number of fields, including adaptive nonlinear control, fault detection and diagnostics, performance analysis, forecasting, knowledge extraction, robotics, behavior modeling.

This paper describes a new method for automatic generation of OWA operators. It introduces a Takagi-Sugeno type model to link the process of selecting the OWA weights to the data being aggregated. A parameterized and cardinality independent type of OWA weighting vector is obtained through an analytically expression of the OWA operator as a function of the derivatives of an S-curve. These results lead to a context dependent information aggregation method.

We present an intelligent control algorithm that is targeted to process control of the steady state of a class of industrial MIMO nonlinear systems. The algorithm, called the RBIC intelligent control algorithm, combines the conventional indirect adaptive control approach with a rule base of initial conditions (RBIC) - an intelligent tool improving the conventional indirect adaptive algorithm in the presence of large disturbances and multiple operating modes. The RBIC operates as an associative memory that periodically reinitializes the indirect adaptive control algorithm by using a fuzzy reasoning inference mechanism. We discuss the main features and application aspects of the RBIC intelligent control algorithm. We also demonstrate one large scale process control application of the RBIC intelligent control algorithm as the main component of Ford Motor Company's integrated paint quality control system.

We discuss the problem of control of zero order MIMO nonlinear systems with transport delay. This problem appears in numerous manufacturing control applications that are characterized with slow dynamics which can be ignored with respect to the sampling rate. We propose three alternative indirect adaptive control algorithms: 1) a conventional application of adaptive control based on a linearized model combining the Kalman filter estimation of a linearized (Jacobian) model with constrained optimization; 2) an intelligent control derived from conventional adaptive control with a linearized model (the first approach) that is integrated with a fuzzy rule-base; and 3) a neural net model (multilayer perceptron) online learning approach. Control updates are calculated by applying a constrained optimization algorithm. All three algorithms are compared and evaluated through simulation of a nonlinear plant with significant transport delay.

The importance as well as the difficulty of the problem of ranking fuzzy numbers is pointed out. Here we consider approaches to the ranking of fuzzy numbers based upon the idea of associating with a fuzzy number a scalar value, its valuation, and using this valuation to compare and order fuzzy numbers. Specifically we focus on expected value type valuations which are based upon the transformation of a fuzzy subset into an associated probability distribution. We develop a number of families of parameterized valuation functions. ©1999 John Wiley & Sons, Inc.

We briefly describe the Ordered Weighted Averaging (OWA) operator and discuss a methodology for learning the associated weighting vector from observational data. We then introduce a more general type of OWA operator called the Induced Ordered Weighted Averaging (IOWA) Operator. These operators take as their argument pairs, called OWA pairs, in which one component is used to induce an ordering over the second components which are then aggregated. A number of different aggregation situations have been shown to be representable in this framework. We then show how this tool can be used to represent different types of aggregation models.

The problem of decision making under doubt is described. the concept of immediate probabilities is introduced. It is seen as a modification of typical probabilistic knowledge with information about the payoffs, mediated through dispositional information (optimism/pessimism), resulting in a modified formulation of an agents perception of the probabilities in effect in the current decision. We use the Dempster rule of combination to help obtain an expression for these probabilities. We show how immediate probabilities allows us to explain the Allais paradox. A number of properties of these probabilities are described. the strategic use of these probabilities are explored as a means for effecting other people's decisions. © 1995 John Wiley & Sons, Inc.

Discusses some basic ideas from the Dempster-Shafer theory of evidence. The authors describe the concept of fuzzy systems modeling used in fuzzy logic control. The authors use the Dempster-Shafer framework to provide a machinery for including randomness in the fuzzy systems modeling process. The authors show how to represent additive noise in this combined framework.>

We develop a simple and effective approach for approximate estimation of the cluster centers on the basis of the concept of a mountain function. We call the procedure the mountain method. It can be useful for obtaining the initial values of the clusters that are required by more complex cluster algorithms. It also can be used as a stand alone simple approximate clustering technique. The method is based upon a griding on the space, the construction of a mountain function from the data and then a destruction of the mountains to obtain the cluster centers.>

We suggest a new approach to the construction of fuzzy logic controllers based upon the selection of systems parameters. We first show that the standard fuzzy logic controllers have four basic operations which determine the nature of their functioning, the aggregation process used to combine individual antecedent firing levels to give a rule firing level, the determination of rule output based on antecedent firing level, the aggregation of individual rule outputs to find combined output, and the defuzzification process. The next show how we can parameterize these operations using S-OWA operators. These parameterized models give us a new class of flexible structured fuzzy logic controllers (FS-FLC). We look at the structure and performance of these controllers. We then suggest that one can improve the structure of fuzzy logic controllers by learning the values of the parameters introduced.>

We discuss the participatory learning model originally introduced by Yager [IEEE Trans. Syst. Man Cybern. SMC-20, 1229–1234 (1990)]. We analyze the learning mechanism as a stable control strategy. We show how the learning mechanism used in participatory learning can be expressed in the form of a fuzzy rule base. We use this rule base formulation to provide new learning rules. We modify the Widrow-Hoff rule to include a participatory learning mechanism. © 1993 John Wiley & Sons, Inc.

We introduce a parameterized family of defuznfica- tion operators called the Semi LInear DEfuzzification (SLIDE) method. This method is based upon a simple transformation of the fuzzy output set of the controller. We suggest an algorithm for the learning of the parameter from a data set. In an attempt to simplify the parameter learning we suggest a modified version of the SLIDE method which results in a simple learning algorithm. The development of the learning algorithm is based upon the use of the Kalman filter N fuzzy logic control systems (l), (2) the defuzzification I step involves the selection of one value as the output of the controller. More specifically, starting with a fuzzy subset (possibility distribution) F over the output space X of the controller, the defuzzification step uses this fuzzy subset to select a representative element x*. The two most often used methods of defuzzification found in the literature are the center of area (COA) and mean of maxima (MOM) (3)-(6) methods. We recall that the MOM method takes as its defuzzified value the mean of the elements that attain the maximum membership grade in F. The COA method takes as its defuzzified value d = Ci(ui * xi), where ui = F(xi)/Cj F(xj). In (7) and (8) we formulated a general defuzzification method via BAsic Defuzzification Distribution (BADD) transformations. The main idea of this BADD approach is to transform the possibility distribution F into a probability distribution P and then the defuzzified value is the expected value of the probability distribution. The process of transforming F into P was seen as a two-step process. The first step was to transform F into a new possibility distribution, E, and then to normalize E to obtain P. The step of obtaining E from F involved the use of a BADD transformation in which E(xi) = (F(z;))~, where 6 E (O,co). It was shown in (7) that the generalized BADD method implies the COA and MOM methods as special cases. In particular the COA method is obtained for a = 1 and the MOM is obtained for 6 = 00. When S = 0 we get a defuzzified value that is the unweighted mean of the output space, d = Xi xi. The BADD transformation has the advantage of being based on a single parameter, which allows us the potential of adaptively learning the best method of defuzzification for a given controller. While the family of all defuzzified values that can be obtained by the generalized BADD defuzzification method was parameterized, an undesirable property of the method was the nonlinear

The unified approach to fuzzy modeling developed in this correspondence addresses the problems of structure and parameter identification of fuzzy models. It demonstrates an alternative view to structure identification, transforming the problem of structure identification to estimation of the distribution of input space. A new concept of sample probability distributions (SPD) is introduced and a family of SPD is constructed. This allows us to simplify the problem of structure identification by replacing identification of membership functions of input variables with identification of the centers of cluster-like regions. The fuzzy model complex of fuzzy model is also discussed in connection with the modeller's confidence and two types of confidence-a priori and a posteriori confidence-are also suggested. The identification problem is solved also under the additional requirement of simplification of the model structure. A learning algorithm realizing structure and parameter identification of quasilinear fuzzy models with the simplest structure is proposed.>

Defuzzification in fuzzy logic controllers concerns itself with the issue of selecting an appropriate crisp value from the fuzzy output of the controller. We provide a parametized family of defuzzification operations. We call this family BAsic Defuzzification Distributions (BADD). We show that the commonly used methods. Mean of Maximum and Center of Area are special cases of this family. We suggest the use of these BADD transformations form the basis of a learning scheme to obtain the optimal defuzzification method in a given application. We suggest that the parameter in the BADD family, the distinction between different defuzzification methods, is related to the confidence we have in the rest of the controller.