We present a technique to investigate abnormal behaviors of signals in both time and frequency domains using an extension of time-frequency logic that uses the continuous wavelet transform. Abnormal signal behaviors such as unexpected oscillations, called hunting behavior, can be challenging to capture in the time domain; however, these behaviors can be naturally captured in the time-frequency domain. We introduce the concept of parametric time-frequency logic and propose a parameter synthesis approach that can be used to classify hunting behavior. We perform a comparative analysis between the proposed algorithm, an approach based on support vector machines using linear classification, and a method that infers a signal temporal logic formula as a data classifier. We present experimental results based on data from a hydrogen fuel cell vehicle application and electrocardiogram data extracted from the MIT-BIH Arrhythmia Database.

A giant leap has been made in the past couple of decades with the introduction of kernel-based learning as a mainstay for designing effective nonlinear computational learning algorithms. In view of the geometric interpretation of conditional expectation and the ubiquity of multiscale characteristics in highly complex nonlinear dynamic systems [1]-[3], this paper presents a new orthogonal projection operator wavelet kernel, aiming at developing an efficient computational learning approach for nonlinear dynamical system identification. In the framework of multiresolution analysis, the proposed projection operator wavelet kernel can fulfill the multiscale, multidimensional learning to estimate complex dependencies. The special advantage of the projection operator wavelet kernel developed in this paper lies in the fact that it has a closed-form expression, which greatly facilitates its application in kernel learning. To the best of our knowledge, it is the first closed-form orthogonal projection wavelet kernel reported in the literature. It provides a link between grid-based wavelets and mesh-free kernel-based methods. Simulation studies for identifying the parallel models of two benchmark nonlinear dynamical systems confirm its superiority in model accuracy and sparsity.

In the Logical Execution Time (LET) programming model, fixed execution times of software tasks are specified and a dedicated middleware is employed to ensure their realization, achieving increased system robustness and predictability. This paradigm has been proposed as a top-down development process, which is hardly applicable to a large body of legacy control software encountered in the embedded industry. Applying LET to legacy software entails challenges such as: satisfying legacy constraints, minimizing additional computational costs, maintaining control quality, and dealing with event-triggered computations. Such challenges are addressed here by a systematic approach, where program analysis and modification techniques are employed to introduce efficient buffering into the legacy system such that the given LET specifications are met. The approach has been implemented in a tool suite that performs fully automated transformation of the legacy software and may be carried out incrementally. This paper presents an application to large-scale automotive embedded software, as well as an evaluation of the achieved LET-based behavior for industrial engine control software.

Industrial control systems are often hybrid systems that are required to satisfy strict performance requirements. Verifying designs against requirements is a difficult task, and there is a lack of suitable open benchmark models to assess, evaluate, and compare tools and techniques. Benchmark models can be valuable for the hybrid systems research community, as they can communicate the nature and complexity of the problems facing industrial practitioners. We present a collection of benchmark problems from the automotive powertrain control domain that are focused on verification for hybrid systems; the problems are intended to challenge the research community while maintaining a manageable scale. We present three models of a fuel control system, each with a unique level of complexity, along with representative requirements in signal temporal logic (STL). We provide results obtained by applying a state of the art analysis tool to these models, and finally, we discuss challenge problems for the research community.

Support vector regression for approximating nonlinear dynamic systems is more delicate than the approximation of indicator functions in support vector classification, particularly for systems that involve multitudes of time scales in their sampled data. The kernel used for support vector learning determines the class of functions from which a support vector machine can draw its solution, and the choice of kernel significantly influences the performance of a support vector machine. In this paper, to bridge the gap between wavelet multiresolution analysis and kernel learning, the closed-form orthogonal wavelet is exploited to construct new multiscale asymmetric orthogonal wavelet kernels for linear programming support vector learning. The closed-form multiscale orthogonal wavelet kernel provides a systematic framework to implement multiscale kernel learning via dyadic dilations and also enables us to represent complex nonlinear dynamics effectively. To demonstrate the superiority of the proposed multiscale wavelet kernel in identifying complex nonlinear dynamic systems, two case studies are presented that aim at building parallel models on benchmark datasets. The development of parallel models that address the long-term/mid-term prediction issue is more intricate and challenging than the identification of series-parallel models where only one-step ahead prediction is required. Simulation results illustrate the effectiveness of the proposed multiscale kernel learning.

As an emerging non-parametric modeling technique, the methodology of support vector regression blazed a new trail in identifying complex nonlinear systems with superior generalization capability and sparsity. Nevertheless, the conventional quadratic programming support vector regression can easily lead to representation redundancy and expensive computational cost. In this paper, by using thel1norm minimization and taking account of the different characteristics of autoregression (AR) and the moving average (MA), an innovative nonlinear dynamical system identification approach, linear programming SVM-ARMA2K, is developed to enhance flexibility and secure model sparsity in identifying nonlinear dynamical systems. To demonstrate the potential and practicality of the proposed approach, the proposed strategy is applied to identify a representative dynamical engine model.

The paper describes the application of an automated verification tool to a software model developed at Ford Motor Company. Ford already has in place an advanced model-based software development framework that employs the Matlab(R), Simulink(R), and Stateflow(R) modeling tools. During this project, we applied the invariant checker Salsa to a Simulink(R)/Stateflow(R) model of automotive software to check for nondeterminism, missing cases, dead code, and redundant code. During the analysis, a number of anomalies were detected that had not been found during manual review. We argue that the detection and correction of these problems demonstrates a cost-effective application of formal verification that elevates our level of confidence in the model.