Nonlinear Scaling Method Research Articles

A Design of Nonlinear Scaling and Nonlinear Optimal Motion Cueing Algorithm for Pilot’s Station

Motion cueing algorithms (MCA) are often applied in the motion simulators. In this paper, a nonlinear optimal MCA, taking into account translational and rotational motions of a simulator within its physical limitation, is designed for the motion platform aiming to minimize human’s perception error in order to provide a high degree of fidelity. Indeed, the movement sensation center of most MCA is placed at the center of the upper platform, which may cause a certain error. Pilot’s station should be paid full attention to in the MCA. Apart from this, the scaling and limiting module plays an important role in optimizing the motion platform workspace and reducing false cues during motion reproduction. It should be used along within the washout filter to decrease the amplitude of the translational and rotational motion signals uniformly across all frequencies through the MCA. A nonlinear scaling method is designed to accurately duplicate motions with high realistic behavior and use the platform more efficiently without violating its physical limitations. The simulation experiment is verified in the longitudinal/pitch direction for motion simulator. The result implies that the proposed method can not only overcome the problem of the workspace limitations in the simulator motion reproduction and improve the realism of movement sensation, but also reduce the false cues to improve dynamic fidelity during the motion simulation process.

Error removal by energy scaling from hyperspectral images for performance improvement of spectral classifiers

ABSTRACT In the remote sensing community, HyperSpectral (HS) images (HSI) are becoming increasingly popular as the advancement of technology and the consequent reduction of cost make them financially more accessible. The reason for their success is the higher capability they can offer, with respect to multispectral data, to discriminate classes that are spectrally similar. A series of pre-processing steps such as geometric, radiometric and atmospheric corrections are carried out on raw data captured by HS sensors. The processed data is then passed to the data analyst, whose work generally relies on the assumption that the received HS data is ‘clean,’ as all possible corrections have already been implemented; however, corrections are hardly perfect and residual disturbances can still bias the quality of results. At this stage, however, all corrections based on ancillary information have already been made and the possibilities for ‘exogenous’ correction of data are exhausted. More could be possibly done by sourcing additional information from the data itself. In this paper, we propose a simple yet effective additional step for error suppression through energy scaling, termed ‘Error Removal by Energy Scaling’ (ERES). In classification problems, the absolute value of wavelength is often overlooked, except for, e.g. removal of strong absorption bands; yet the value can actually further support the classification process if their physical meaning is tapped. The proposed ERES method is indeed a non-linear scaling method, derived from physical phenomena linked with radiation extinction properties. In ERES, each band is associated with an energy level, that is inversely related to its own wavelength. The associated nonlinear energy information in HSI, neglected in most classification strategies, prevents optimal separation of class-specific spectral signatures, that are generated by the physics of wave-matter interaction. This is especially true for linear classifiers such as Support Vector Machines (SVM). Removing this physics-linked information makes data more suitable to be classified with physics-unaware classification strategies, typically used in down stream remotely sensed data processing. The relevance of the issue, and the benefits of ERES, are discussed and validated in this work over three different datasets, using accuracy improvements on the popular Spectral Angle Mapper and SVM classifiers as a means to gauge the effectiveness of the correction strategy. Results clearly reveal the positive impact of applying ERES to the data before proceeding to classification.

Scaling and characterisation of a 2-DoF velocity amplified electromagnetic vibration energy harvester

Vibration energy harvesters (VEHs) offer an alternative to batteries for the autonomous operation of low-power electronics. Understanding the influence of scaling on VEHs is of great importance in the design of reduced scale harvesters. The nonlinear harvesters investigated here employ velocity amplification, a technique used to increase velocity through impacts, to improve the power output of multiple-degree-of-freedom VEHs, compared to linear resonators. Such harvesters, employing electromagnetic induction, are referred to as velocity amplified electromagnetic generators (VAEGs), with gains in power achieved by increasing the relative velocity between the magnet and coil in the transducer. The influence of scaling on a nonlinear 2-DoF VAEG is presented. Due to the increased complexity of VAEGs, compared to linear systems, linear scaling theory cannot be directly applied to VAEGs. Therefore, a detailed nonlinear scaling method is utilised. Experimental and numerical methods are employed. This nonlinear scaling method can be used for analysing the scaling behaviour of all nonlinear electromagnetic VEHs. It is demonstrated that the electromagnetic coupling coefficient degrades more rapidly with scale for systems with larger displacement amplitudes, meaning that systems operating at low frequencies will scale poorly compared to those operating at higher frequencies. The load power of the 2-DoF VAEG is predicted to scale as (s = volume1/3), suggesting that achieving high power densities in a VAEG with low device volume is extremely challenging.

A genetic algorithm–based nonlinear scaling method for optimal motion cueing algorithm in driving simulator

A motion cueing algorithm plays an important role in generating motion cues in driving simulators. The motion cueing algorithm is used to transform the linear acceleration and angular velocity of a vehicle into the translational and rotational motions of a simulator within its physical limitation through washout filters. Indeed, scaling and limiting should be used along within the washout filter to decrease the amplitude of the translational and rotational motion signals uniformly across all frequencies through the motion cueing algorithm. This is to decrease the effects of the workspace limitations in the simulator motion reproduction and improve the realism of movement sensation. A nonlinear scaling method based on the genetic algorithm for the motion cueing algorithm is developed in this study. The aim is to accurately produce motions with a high degree of fidelity and use the platform more efficiently without violating its physical limitations. To successfully achieve this aim, a third-order polynomial scaling method based on the genetic algorithm is formulated, tuned, and implemented for the linear quadratic regulator–based optimal motion cueing algorithm. A number of factors, which include the sensation error between the real and simulator drivers, the simulator’s physical limitations, and the sensation signal shape-following criteria, are considered in optimizing the proposed nonlinear scaling method. The results show that the proposed method not only is able to overcome problems pertaining to selecting nonlinear scaling parameters based on trial-and-error and inefficient usage of the platform workspace, but also to reduce the sensation error between the simulator and real drivers, while satisfying the constraints imposed by the platform boundaries.

Non-linear scaling of a musculoskeletal model of the lower limb using statistical shape models

Accurate muscle geometry for musculoskeletal models is important to enable accurate subject-specific simulations. Commonly, linear scaling is used to obtain individualised muscle geometry. More advanced methods include non-linear scaling using segmented bone surfaces and manual or semi-automatic digitisation of muscle paths from medical images. In this study, a new scaling method combining non-linear scaling with reconstructions of bone surfaces using statistical shape modelling is presented. Statistical Shape Models (SSMs) of femur and tibia/fibula were used to reconstruct bone surfaces of nine subjects. Reference models were created by morphing manually digitised muscle paths to mean shapes of the SSMs using non-linear transformations and inter-subject variability was calculated. Subject-specific models of muscle attachment and via points were created from three reference models. The accuracy was evaluated by calculating the differences between the scaled and manually digitised models. The points defining the muscle paths showed large inter-subject variability at the thigh and shank – up to 26mm; this was found to limit the accuracy of all studied scaling methods. Errors for the subject-specific muscle point reconstructions of the thigh could be decreased by 9% to 20% by using the non-linear scaling compared to a typical linear scaling method. We conclude that the proposed non-linear scaling method is more accurate than linear scaling methods. Thus, when combined with the ability to reconstruct bone surfaces from incomplete or scattered geometry data using statistical shape models our proposed method is an alternative to linear scaling methods.

Predicting the residual aluminum level in water treatment process

Abstract. In water treatment processes, aluminum salts are widely used as coagulation chemical. High dose of aluminum has been proved to be at least a minor health risk and some evidence points out that aluminum could increase the risk of Alzheimer's disease. Thus it is important to minimize the amount of residual aluminum in drinking water and water used at food industry. In this study, the data of a water treatment plant (WTP) was analyzed and the residual aluminum in drinking water was predicted using Multiple Linear Regression (MLR) and Artificial Neural Network (ANN) models. The purpose was to find out which variables affect the amount of residual aluminum and create simple and reliable prediction models which can be used in an early warning system (EWS). Accuracy of ANN and MLR models were compared. The new nonlinear scaling method based on generalized norms and skewness was used to scale all measurement variables to range [−2...+2] before data-analysis and modeling. The effect of data pre-processing was studied by comparing prediction results to ones achieved in an earlier study. Results showed that it is possible to predict the baseline level of residual aluminum in drinking water with a simple model. Variables that affected the most the amount of residual aluminum were among others: raw water temperature, raw water KMnO4 and PAC/KMnO4 (Poly-Aluminum Chloride/Potassium permanganate)-ratio. The accuracies of MLR and ANN models were found to be almost the same. Study also showed that data pre-processing affects to the final prediction result.

Nonlinear Scaling Relationships of a Railgun

Scaling methods are widely used in railgun technology. But nonlinear problems are seldom studied because of the complexity and uncertainty. To employ the scaling method better, this paper brings the nonlinear drag model to the solid armature railgun circuit. Several drag models are compared including friction drag model (FDM), atmosphere drag model (ADM), and current drag model (CDM). Then, nonlinear scaling relationships of these drag models are discussed. Furthermore, a novel experiment is constructed to compare the drag models at low velocity. At last, the nonlinear scaling method is verified by an example at high velocity. FDM is accurate enough to simulate a railgun system at any condition. Coefficient $\varepsilon$ in FDM should be used considering different test conditions. Scaling relationships of FDM could not be derived at low velocity because of nonlinearity. Although at high velocity, FDM could be simplified to CDM and realize linear scaling method (LSM). Further research indicates that the FDM could use the scaling method directly and realize approximate LSM. CDM is workable which satisfies the conditions of LSM in nature. Due to the work range of the solid armature, usually under 2.5 km/s, nonlinear scaling method could be used in a railgun with FDM. For a solid armature railgun, the $f_{\rm ADM}$ is too small compared with $f_{\rm FDM}$ and it could be ignored in analysis of a railgun, especially at low velocity. What should be noted is that the velocity scaling factor must be controlled above about one-quarter to avoid the nonlinear field.

Two Mitigation Strategies for Motion System Limits in Driving and Flight Simulators

Limited workspace is a challenge for all motion-based simulators, whether they are large excursion systems like the National Advanced Driving Simulator or smaller simulators utilizing only Stewart Platforms. Two approaches for addressing this challenge are nonlinear washout scaling and software displacement limiting. This paper presents new algorithms developed for these approaches. The nonlinear scaling method uses the cubic Hermite interpolation polynomial to smooth the corner in the scaled output at the limit. A software displacement limiting method that generates control signals in the table frame of reference is introduced. As a result, unwanted acceleration artifacts caused by unbalanced limiting of actuators are avoided. The methods are described, and offline simulation results using the new displacement limiting method are presented.