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In many industrial applications a workpiece is continuously fed through a heating zone in order to reach a desired temperature to obtain specific material properties. Many examples of such distributed parameter systems exist in heavy industry and also in furniture production such processes can be found. In this paper, a real-time capable model for a heating process with application to industrial furniture production is modeled. As the model is intended to be used in a Model Predictive Control (MPC) application, the main focus is to achieve minimum computational runtime while maintaining a sufficient amount of accuracy. Thus, the governing Partial Differential Equation (PDE) is discretized using finite differences on a grid, specifically tailored to this application. The grid is optimized to yield acceptable accuracy with a minimum number of grid nodes such that a relatively low order model is obtained. Subsequently, an explicit Runge-Kutta ODE (Ordinary Differential Equation) solver of fourth order is compared to the Crank-Nicolson integration scheme presented in Weiss et al. (2022) in terms of runtime and accuracy. Finally, the unknown thermal parameters of the process are estimated using real-world measurement data that was obtained from an experimental setup. The final model yields acceptable accuracy while at the same time shows promising computation time, which enables its use in an MPC controller.
This paper presents a modeling approach of an industrial heating process where a stripe-shaped workpiece is heated up to a specific temperature by applying hot air through a nozzle. The workpiece is moving through the heating zone and is considered to be of infinite length. The speed of the substrate is varying over time. The derived model is supposed to be computationally cheap to enable its use in a model-based control setting. We start by formulating the governing PDE and the corresponding boundary conditions. The PDE is then discretized on a spatial grid using finite differences and two different integration schemes, explicit and implicit, are derived. The two models are evaluated in terms of computational effort and accuracy. It turns out that the implicit approach is favorable for the regarded process. We optimize the grid of the model to achieve a low number of grid nodes while maintaining a sufficient amount of accuracy. Finally, the thermodynamical parameters are optimized in order to fit the model's output to real-world data that was obtained by experiments.
In this letter, we present an approach to building a new generalized multistream spatial modulation system (GMSM), where the information is conveyed by the two active antennas with signal indices and using all possible active antenna combinations. The signal constellations associated with these antennas may have different sizes. In addition, four-dimensional hybrid frequency-phase modulated signals are utilized in GMSM. Examples of GMSM systems are given and computer simulation results are presented for transmission over Rayleigh and deep Nakagami- m flat-fading channels when maximum-likelihood detection is used. The presented results indicate a significant improvement of characteristics compared to the best-known similar systems.
Code-based cryptosystems are promising candidates for post-quantum cryptography. Recently, generalized concatenated codes over Gaussian and Eisenstein integers were proposed for those systems. For a channel model with errors of restricted weight, those q-ary codes lead to high error correction capabilities. Hence, these codes achieve high work factors for information set decoding attacks. In this work, we adapt this concept to codes for the weight-one error channel, i.e., a binary channel model where at most one bit-error occurs in each block of m bits. We also propose a low complexity decoding algorithm for the proposed codes. Compared to codes over Gaussian and Eisenstein integers, these codes achieve higher minimum Hamming distances for the dual codes of the inner component codes. This property increases the work factor for a structural attack on concatenated codes leading to higher overall security. For comparable security, the key size for the proposed code construction is significantly smaller than for the classic McEliece scheme based on Goppa codes.
Code-based cryptography is a promising candidate for post-quantum public-key encryption. The classic McEliece system uses binary Goppa codes, which are known for their good error correction capability. However, the key generation and decoding procedures of the classic McEliece system have a high computation complexity. Recently, q-ary concatenated codes over Gaussian integers were proposed for the McEliece cryptosystem together with the one-Mannheim error channel, where the error values are limited to Mannheim weight one. For this channel, concatenated codes over Gaussian integers achieve a higher error correction capability than maximum distance separable (MDS) codes with bounded minimum distance decoding. This improves the work factor regarding decoding attacks based on information-set decoding. This work proposes an improved construction for codes over Gaussian integers. These generalized concatenated codes extent the rate region where the work factor is beneficial compared to MDS codes. They allow for shorter public keys for the same level of security as the classic Goppa codes. Such codes are beneficial for lightweight code-based cryptosystems.
Large-scale quantum computers threaten today's public-key cryptosystems. The code-based McEliece and Niederreiter cryptosystems are among the most promising candidates for post-quantum cryptography. Recently, a new class of q-ary product codes over Gaussian integers together with an efficient decoding algorithm were proposed for the McEliece cryptosystems. It was shown that these codes achieve a higher work factor for information-set decoding attacks than maximum distance separable (MDS) codes with comparable length and dimension. In this work, we adapt this q-ary product code construction to codes over Eisenstein integers. We propose a new syndrome decoding method which is applicable for Niederreiter cryptosystems. The code parameters and work factors for information-set decoding are comparable to codes over Gaussian integers. Hence, the new construction is not favorable for the McEliece system. Nevertheless, it is beneficial for the Niederreiter system, where it achieves larger message lengths. While the Niederreiter and McEliece systems have the same level of security, the Niederreiter system can be advantageous for some applications, e.g., it enables digital signatures. The proposed coding scheme is interesting for lightweight Niederreiter cryptosystems and embedded security due to the short code lengths and low decoding complexity.
The code-based McEliece cryptosystem is a promising candidate for post-quantum cryptography. The sender encodes a message, using a public scrambled generator matrix, and adds a random error vector. In this work, we consider q-ary codes and restrict the Lee weight of the added error symbols. This leads to an increased error correction capability and a larger work factor for information-set decoding attacks. In particular, we consider codes over an extension field and use the one-Lee error channel, which restricts the error values to Lee weight one. For this channel model, generalized concatenated codes can achieve high error correction capabilities. We discuss the decoding of those codes and the possible gain for decoding beyond the guaranteed error correction capability.
Nowadays, most digital modulation schemes are based on conventional signal constellations that have no algebraic group, ring, or field properties, e.g. square quadrature-amplitude modulation constellations. Signal constellations with algebraic structure can enhance the system performance. For instance, multidimensional signal constellations based on dense lattices can achieve performance gains due to the dense packing. The algebraic structure enables low-complexity decoding and detection schemes. In this work, signal constellations with algebraic properties and their application in spatial modulation transmission schemes are investigated. Several design approaches of two- and four-dimensional signal constellations based on Gaussian, Eisenstein, and Hurwitz integers are shown. Detection algorithms with reduced complexity are proposed. It is shown, that the proposed Eisenstein and Hurwitz constellations combined with the proposed suboptimal detection can outperform conventional two-dimensional constellations with ML detection.
Reliability Assessment of an Unscented Kalman Filter by Using Ellipsoidal Enclosure Techniques
(2022)
The Unscented Kalman Filter (UKF) is widely used for the state, disturbance, and parameter estimation of nonlinear dynamic systems, for which both process and measurement uncertainties are represented in a probabilistic form. Although the UKF can often be shown to be more reliable for nonlinear processes than the linearization-based Extended Kalman Filter (EKF) due to the enhanced approximation capabilities of its underlying probability distribution, it is not a priori obvious whether its strategy for selecting sigma points is sufficiently accurate to handle nonlinearities in the system dynamics and output equations. Such inaccuracies may arise for sufficiently strong nonlinearities in combination with large state, disturbance, and parameter covariances. Then, computationally more demanding approaches such as particle filters or the representation of (multi-modal) probability densities with the help of (Gaussian) mixture representations are possible ways to resolve this issue. To detect cases in a systematic manner that are not reliably handled by a standard EKF or UKF, this paper proposes the computation of outer bounds for state domains that are compatible with a certain percentage of confidence under the assumption of normally distributed states with the help of a set-based ellipsoidal calculus. The practical applicability of this approach is demonstrated for the estimation of state variables and parameters for the nonlinear dynamics of an unmanned surface vessel (USV).
Experimental Validation of Ellipsoidal Techniques for State Estimation in Marine Applications
(2022)
A reliable quantification of the worst-case influence of model uncertainty and external disturbances is crucial for the localization of vessels in marine applications. This is especially true if uncertain GPS-based position measurements are used to update predicted vessel locations that are obtained from the evaluation of a ship’s state equation. To reflect real-life working conditions, these state equations need to account for uncertainty in the system model, such as imperfect actuation and external disturbances due to effects such as wind and currents. As an application scenario, the GPS-based localization of autonomous DDboat robots is considered in this paper. Using experimental data, the efficiency of an ellipsoidal approach, which exploits a bounded-error representation of disturbances and uncertainties, is demonstrated.