Computational Load Requirements Research Articles

Low rank approximation method for perturbed linear systems with applications to elliptic type stochastic PDEs

In this paper, we propose a low rank approximation method for efficiently solving stochastic partial differential equations. Specifically, our method utilizes a novel low rank approximation of the stiffness matrices, which can significantly reduce the computational load and storage requirements associated with matrix inversion without losing accuracy. To demonstrate the versatility and applicability of our method, we apply it to address two crucial uncertainty quantification problems: stochastic elliptic equations and optimal control problems governed by stochastic elliptic PDE constraints. Based on varying dimension reduction ratios, our algorithm exhibits the capability to yield a high-precision numerical solution for stochastic partial differential equations, or provides a rough representation of the exact solutions as a pre-processing phase. Meanwhile, our algorithm for solving stochastic optimal control problems allows a diverse range of gradient-based unconstrained optimization methods, rendering it particularly appealing for computationally intensive large-scale problems. Numerical experiments are conducted and the results provide strong validation of the feasibility and effectiveness of our algorithm.

A Piecewise Particle Swarm Optimisation Modelling Method for Pneumatic Artificial Muscle Actuators

Pneumatic artificial muscles (PAMs) possess compliant properties desirable for certain applications such as prosthetics and robotic structures. However, this compliance along with their inherent nonlinear dynamics make them difficult to accurately model and as such accurately control under certain control architectures. Common approaches to this problem include measuring the actuator’s physical properties and approximating a model based on these parameters or using deep learning methods to train a model with the actuator’s behaviours. This paper introduces an optimisation-based modelling approach based on a particle swarm optimisation (PSO) algorithm using a mass–spring–damper approximation for the PAM, as well as a piecewise modelling method that accounts for nonlinear dynamics. The use of optimisation to estimate model parameters removes the need to measure physical properties, and the three-element approximation allows for fast model generation with low computational complexity and training data requirements. Through multiple tests comparing model behaviour with real PAM motion, the accuracy of these models is confirmed to be promising for future work. Dynamic nonlinearities are properly accounted for using the piecewise modelling method, including both hysteresis and disproportionate input/output relationship across the stroke length of the actuator. Compared with other PAM modelling techniques, this method has improved generation time, lower computational load requirements, and complexity and can be applied to actuators for which the phenomenological mass–spring–damper model is a good approximation.

A Homomorphic Encryption Framework for Privacy-Preserving Spiking Neural Networks

Machine learning (ML) is widely used today, especially through deep neural networks (DNNs); however, increasing computational load and resource requirements have led to cloud-based solutions. To address this problem, a new generation of networks has emerged called spiking neural networks (SNNs), which mimic the behavior of the human brain to improve efficiency and reduce energy consumption. These networks often process large amounts of sensitive information, such as confidential data, and thus privacy issues arise. Homomorphic encryption (HE) offers a solution, allowing calculations to be performed on encrypted data without decrypting them. This research compares traditional DNNs and SNNs using the Brakerski/Fan-Vercauteren (BFV) encryption scheme. The LeNet-5 and AlexNet models, widely-used convolutional architectures, are used for both DNN and SNN models based on their respective architectures, and the networks are trained and compared using the FashionMNIST dataset. The results show that SNNs using HE achieve up to 40% higher accuracy than DNNs for low values of the plaintext modulus t, although their execution time is longer due to their time-coding nature with multiple time steps.

Fast Helmet and License Plate Detection Based on Lightweight YOLOv5.

The integrated fast detection technology for electric bikes, riders, helmets, and license plates is of great significance for maintaining traffic safety. YOLOv5 is one of the most advanced single-stage object detection algorithms. However, it is difficult to deploy on embedded systems, such as unmanned aerial vehicles (UAV), with limited memory and computing resources because of high computational load and high memory requirements. In this paper, a lightweight YOLOv5 model (SG-YOLOv5) is proposed for the fast detection of the helmet and license plate of electric bikes, by introducing two mechanisms to improve the original YOLOv5. Firstly, the YOLOv5s backbone network and the Neck part are lightened by combining the two lightweight networks, ShuffleNetv2 and GhostNet, included. Secondly, by adopting an Add-based feature fusion method, the number of parameters and the floating-point operations (FLOPs) are effectively reduced. On this basis, a scene-based non-truth suppression method is proposed to eliminate the interference of pedestrian heads and license plates on parked vehicles, and then the license plates of the riders without helmets can be located through the inclusion relation of the target boxes and can be extracted. To verify the performance of the SG-YOLOv5, the experiments are conducted on a homemade RHNP dataset, which contains four categories: rider, helmet, no-helmet, and license plate. The results show that, the SG-YOLOv5 has the same mean average precision (mAP0.5) as the original; the number of model parameters, the FLOPs, and the model file size are reduced by 90.8%, 80.5%, and 88.8%, respectively. Additionally, the number of frames per second (FPS) is 2.7 times higher than that of the original. Therefore, the proposed SG-YOLOv5 can effectively achieve the purpose of lightweight and improve the detection speed while maintaining great detection accuracy.

Navigation With Time Limits in Transportation Networks: A Fourth Moment Approach

This paper investigates the stochastic on-time arrival (SOTA) problem in transportation networks. We propose a fourth moment approach (FMA), which calculates the tight lower bound of a given routing policy’s on-time-arrival probability, through estimating the first four moments of the policy’s travel time. Then, we employ the generalized policy iteration (GPI) scheme to gradually improve the policy towards the optimal one. Different from state-of-the-art algorithms for the SOTA problem, which require the full travel time distribution and usually incur high computational cost due to the convolution integration operation, FMA only requires the moments of travel-time statistics, which are easily estimated from the statistics perspective. Moreover, the algorithm’s computational complexity analysis indicates the relatively light computational load requirement of FMA. Experimental results in a range of transportation networks show FMA’s superior performance over state of the arts.

Physics-based digital twins for autonomous thermal food processing: Efficient, non-intrusive reduced-order modeling

One possible way of making thermal processing controllable is to gather real-time information on the product's current state. Often, sensory equipment cannot capture all relevant information easily or at all. Digital Twins close this gap with virtual probes in real-time simulations, synchronized with the process. This paper proposes a physics-based, data-driven Digital Twin framework for autonomous food processing. We suggest a lean Digital Twin concept that is executable at the device level, entailing minimal computational load, data storage, and sensor data requirements. This study focuses on a parsimonious experimental design for training non-intrusive reduced-order models (ROMs) of a thermal process. A correlation (R = − 0.76) between a high standard deviation of the surface temperatures in the training data and a low root mean square error in ROM testing enables efficient selection of training data. The mean test root mean square error of the best ROM is less than 1 Kelvin (0.2% mean average percentage error) on representative test sets. Simulation speed-ups of Sp ≈ 1.8 × 104 allow on-device model predictive control. Industrial relevanceThe proposed Digital Twin framework is designed to be applicable within the industry. Typically, non-intrusive reduced-order modeling is required as soon as the modeling of the process is performed in software, where root-level access to the solver is not provided, such as commercial simulation software. The data-driven training of the reduced-order model is achieved with only one data set, as correlations are utilized to predict the training success a priori.

Signal recovery from a few linear measurements of its high-order spectra

The q -th order spectrum is a polynomial of degree q in the entries of a signal x ∈ C N , which is invariant under circular shifts of the signal. For q ≥ 3 , this polynomial determines the signal uniquely, up to a circular shift, and is called a high-order spectrum. The high-order spectra, and in particular the bispectrum ( q = 3 ) and the trispectrum ( q = 4 ), play a prominent role in various statistical signal processing and imaging applications, such as phase retrieval and single-particle reconstruction. However, the dimension of the q -th order spectrum is N q − 1 , far exceeding the dimension of x , leading to increased computational load and storage requirements. In this work, we show that it is unnecessary to store and process the full high-order spectra: a signal can be uniquely characterized up to symmetries, from only N + 1 linear measurements of its high-order spectra. The proof relies on tools from algebraic geometry and is corroborated by numerical experiments.

Optimised elliptic curve digital signature on NIST compliant curves for authentication of MANET nodes

Secure routing protocols for mobile ad hoc networks (MANETs) use digital signatures for authentication which increases computational and communication overheads. Elliptical curve digital signature (ECDSA) uses much shorter keys resulting in smaller signatures, lower computational load, less memory and power requirements which are crucial to MANET nodes. The ECDSA has a characteristic that the signature generation is very fast but signature verification takes much longer time. Optimisation of point operations and scalar multiplication of points have been proposed for accelerating the signature generation and verification process. The proposed method has been software implemented by writing the code in Java using Big-integer class on a Linux platform for National Institute of Standards and Technology (NIST) compliant curves and has accelerated the signature verification process of ECDSA by approximately 27% over the sequential mixed Jacobian-Affine NAF scalar multiplication method of verification.

Optimised elliptic curve digital signature on NIST compliant curves for authentication of MANET nodes

Secure routing protocols for mobile ad hoc networks (MANETs) use digital signatures for authentication which increases computational and communication overheads. Elliptical curve digital signature (ECDSA) uses much shorter keys resulting in smaller signatures, lower computational load, less memory and power requirements which are crucial to MANET nodes. The ECDSA has a characteristic that the signature generation is very fast but signature verification takes much longer time. Optimisation of point operations and scalar multiplication of points have been proposed for accelerating the signature generation and verification process. The proposed method has been software implemented by writing the code in Java using Big-integer class on a Linux platform for National Institute of Standards and Technology (NIST) compliant curves and has accelerated the signature verification process of ECDSA by approximately 27% over the sequential mixed Jacobian-Affine NAF scalar multiplication method of verification.

Segment-sliding reconstruction of pulsed radar echoes with sub-Nyquist sampling

It has been shown that analog-to-information conversion (AIC) is an efficient scheme to perform sub-Nyquist sampling of pulsed radar echoes. However, it is often impractical, if not infeasible, to reconstruct full-range Nyquist samples because of huge storage and computational load requirements. Based on the analyses of AIC measurement system, this paper develops a novel segment-sliding reconstruction (SegSR) scheme to effectively reconstruct the Nyquist samples. The SegSR performs segment-by-segment reconstruction in a sliding mode and can be implemented in real time. An important characteristic that distinguishes the proposed SegSR from existing methods is that the measurement matrix in each segment satisfies the restricted isometry property (RIP) condition. Partial support in the previous segment can be incorporated into the estimation of the Nyquist samples in the current segment. The effect of interference introduced from adjacent segments is theoretically analyzed, and it is revealed that the interference consists of two interference levels with different impacts to the signal reconstruction performance. With these observations, a two-step orthogonal matching pursuit (OMP) procedure is proposed for segment reconstruction, which takes into account different interference levels and partially known support of the previous segment. The proposed SegSR scheme achieves near-optimal reconstruction performance with a significant reduction of computational loads and storage requirements. Theoretical analyses and simulations verify its effectiveness.

Fast nonparaxial scalar focal field calculations.

An efficient algorithm for calculating nonparaxial scalar field distributions in the focal region of a lens is discussed. The algorithm is based on fast Fourier transform implementations of the first Rayleigh-Sommerfeld diffraction integral and assumes that the input field at the pupil plane has a larger extent than the field in the focal region. A sampling grid is defined over a finite region in the output plane and referred to as a tile. The input field is divided into multiple separate spatial regions of the size of the output tile. Finally, the input tiles are added coherently to form a summed tile, which is propagated to the output plane. Since only a single tile is propagated, there are significant reductions of computational load and memory requirements. This method is combined either with a subpixel sampling technique or with a chirp z-transform to realize smaller sampling intervals in the output plane than in the input plane. For a given example the resulting methods enable a speedup of approximately 800× in comparison to the normal angular spectrum method, while the memory requirements are reduced by more than 99%.

Vehicle Yaw Stability Control by Coordinated Active Front Steering and Differential Braking in the Tire Sideslip Angles Domain

Vehicle active safety receives ever increasing attention in the attempt to achieve zero accidents on the road. In this paper, we investigate a control architecture that has the potential of improving yaw stability control by achieving faster convergence and reduced impact on the longitudinal dynamics. We consider a system where active front steering and differential braking are available and propose a model predictive control (MPC) strategy to coordinate the actuators. We formulate the vehicle dynamics with respect to the tire slip angles and use a piecewise affine (PWA) approximation of the tire force characteristics. The resulting PWA system is used as prediction model in a hybrid MPC strategy. After assessing the benefits of the proposed approach, we synthesize the controller by using a switched MPC strategy, where the tire conditions (linear/saturated) are assumed not to change during the prediction horizon. The assessment of the controller computational load and memory requirements indicates that it is capable of real-time execution in automotive-grade electronic control units. Experimental tests in different maneuvers executed on low-friction surfaces demonstrate the high performance of the controller.

Fuzzy logic control implementation considerations and complexity analyses

In this paper, a number of implementation and algorithmic options for fuzzy logic control applications are presented. The emphases are on the analyses of the computational load and memory requirements of all the processing stages of fuzzy logic control algorithms. Comparisons are made among commonly used techniques and recommendations are provided. The results could be used to guide the design of fuzzy logic controllers for an embedded or hardware implementation.

Adaptive Estimation of Difficult-to-Measure Process Variables

There exist many problems regarding process control in the process industry since some of the important variables cannot be measured online. This problem can be significantly solved by estimating these difficult-to-measure process variables. In doing so, the estimator is in fact an appropriate mathematical model of the process which, based on information about easy-to-measure process variables, estimates the current value of the difficult- to-measure variable. Since processes are usually time-varying, the precision of the estimation based on the process model which is built on old data is decreasing over time. To avoid estimator accuracy degradation, model parameters should be continuously updated in order to track process behavior. There are a couple of methods available for updating model parameters depending on the type of process model. In this paper, PLSR process model is chosen as the basis of the difficult-to-measure process variable estimator while its parameters are updated in several ways—by the moving window method, recursive NIPALS algorithm, recursive kernel algorithm and Just-in-Time learning algorithm. Properties of these adaptive methods are explored on a simulated example. Additionally, the methods are analyzed in terms of computational load and memory requirements.

A Low Complexity Two-Stage Target Detection Scheme for Resource Limited Radar Systems

A two-stage detector is proposed to accommodate high computational load requirements of modern radar systems. The first stage of the proposed system is a low-complexity detector that operates at an unusually high false alarm probability value around 1/10. This stage is to prescreen and eliminate some of the test cells with relatively few operations. The second stage operates only on the cells passing the prescreening stage and implements a high-complexity detector at a desired system false alarm rate. Due to the detector cascade, the second stage has a large amount of computational load reduction, on the order of 10 folds, in comparison with the single-stage systems. The mathematical analysis of the described two-stage detector is presented, and the relations for the false alarm and detection probability are derived. The numerical results show that it is possible to achieve a significant computational load reduction at a negligible performance loss with the proper selection of detector parameters.

Global and Fast Receiver Antenna Selection for MIMO Systems

For a multiple-input multiple-output (MIMO) system with more antennas at the receiver than the transmitter, selecting the same number of receiver antennas as the number of transmit antennas captures most of the advantages of MIMO capacity performance and reduces the system hardware and computational cost at the same time. In this paper, a fast and global-search receive antenna selection algorithm is proposed for this MIMO array configuration. Different from many existing fast but `local' antenna selection algorithms which obtain the sub-optimal channel submatrix by adding or removing one row per step, our algorithm acquires the near-optimal channel matrix by {directly} and {rapidly} the maximum-volume submatrix of the original channel matrix. Due to its globally searching property, our antenna selection algorithm leads to a substantial improvement in the capacity optimality for moderate to high SNRs, and obtains almost the same capacity performance as that of the exhaustive-search-based optimal antenna selection algorithm. Furthermore, the computational load and memory requirement for our antenna selection method are still comparable to those of the existing sub-optimal antenna selection methods. Numerical results are provided to verify the validity of the proposed methods.

Global and Fast Receiver Antenna Selection for MIMO Systems

For a multiple-input multiple-output (MIMO) system with more antennas at the receiver than the transmitter, selecting the same number of receiver antennas as the number of transmit antennas captures most of the advantages of MIMO capacity performance and reduces the system hardware and computational cost at the same time. In this paper, a fast and global-search receive antenna selection algorithm is proposed for this MIMO array configuration. Different from many existing fast but `local' antenna selection algorithms which obtain the sub-optimal channel submatrix by adding or removing one row per step, our algorithm acquires the near-optimal channel matrix by {directly} and {rapidly} searching the maximum-volume submatrix of the original channel matrix. Due to its "globally searching" property, our antenna selection algorithm leads to a substantial improvement in the capacity optimality for moderate to high SNRs, and obtains almost the same capacity performance as that of the exhaustive-search-based optimal antenna selection algorithm. Furthermore, the computational load and memory requirement for our antenna selection method are still comparable to those of the existing sub-optimal antenna selection methods. Numerical results are provided to verify the validity of the proposed methods.

In-Flight Attitude Perturbation Estimation for Earth-Orbiting Spacecraft

This paper presents four innovative techniques, three Kalman-based and one observer-based, to estimate environmental perturbation torques acting on an Earth-orbiting spacecraft. The Kalman-based techniques all use simple generic models for the state dependence of the perturbation, and for estimating the unknown coefficients included in these generic mathematical formulations. The observer-based technique is developed with the nonlinear disturbance observer theory. The proposed strategies are validated in numerical simulations and are traded-off in terms of estimation accuracy and computational load requirement. Then, the most suitable estimation technique is combined with a batch least square filter algorithm to yield a perturbation estimation system with low computational load, which can be implemented onboard a spacecraft. Finally, the proposed estimation strategy is applied to a realistic gyroless Earth-orbiting spacecraft mission: the European Space Agency’s Project for Onboard Autonomy (PROBA)-2 mission. Ultimately, the selected estimation strategy will be implemented onboard the PROBA-2 spacecraft for in-flight validation. All strategies proposed in this article are general and are applicable to any Earth-orbiting spacecraft.

An efficient low cost approach for on-line signature recognition based on length normalization and fractional distances

This work presents a new proposal for an efficient on-line signature recognition system with very low computational load and storage requirements, suitable to be used in resource-limited systems like smart-cards. The novelty of the proposal is in both the feature extraction and classification stages, since it is based on the use of size normalized signatures, which allows for similarity estimation, usually based on dynamic time warping (DTW) or hidden Markov models (HMMs), to be performed by an easy distance calculation between vectors, which is computed using fractional distance, instead of the more typical Euclidean one, so as to overcome the concentration phenomenon that appears when data are high dimensional. Verification and identification tasks have been carried out using the MCYT database, achieving an EER (common threshold) of 6.6% and 1.8% with skilled and random forgeries, respectively, in the first task and 3.6% of error in the second. The proposed system outperforms DTW-based and HMM-based ones, even though these have proved to be very efficient in on-line signature recognition, with storage requirements between 9 and 90 times lesser and a processing speed between 181 and 713 times greater than the DTW-based systems.

Comparison of generalized phase contrast and computer generated holography for laser image projection

Laser projection based on phase modulation promises several advantages over amplitude modulation. We examine and compare the merits of two phase modulation techniques; phase-only computer generated holography and generalized phase contrast, for the application of dynamic laser image projection. We adopt information theory as a guiding framework and analyze information-relevant metrics such as space-bandwidth product, output display resolution, efficiency, speckle noise, computational load and device requirements. The analysis takes into account the perspective of potential end-users.