Nonlinear Input-output Relationship Research Articles

Rotor dynamic response prediction using physics-informed multi-LSTM networks

The deep learning method provides an effective alternative to numerical simulations for establishing the nonlinear input-output relationship and calculating dynamic responses of rotor systems. To overcome the low generalization capability of pure data-driven long short-term memory (LSTM) networks when predicting dynamic responses to out-of-distribution inputs, a dynamic response prediction method using physics-informed multi-LSTM networks is proposed. This approach incorporates required physical constraints into the deep LSTM network, allowing the model training process to optimize the network parameters within the feasible solution space that adheres to physical laws. Consequently, this enhances the physical interpretability of the deep learning model. Specifically, two physics-informed multi-LSTM network architectures are introduced, and physical laws of equation of motion, state dependency and hysteretic constitutive relationship are considered to construct the physics loss. The feasibility of the proposed method is verified by a Bouc-Wen hysteresis model and a simulated gas generator rotor. The response prediction performance of the two networks is validated on a constructed fault rotor dataset with significant sample differences, along with cross-speed and cross-node prediction validation for the rotor system. The results demonstrate that the trained networks exhibit strong robustness and generalization capabilities, making them suitable as surrogate models for rotor systems.

Numerical algorithm for nonlinearity compensation of hardly constrained actuation for trajectory tracking control of deadzone-included dynamic systems

This paper addresses the control of a nonlinear system affected by deadzone effects, using a constrained actuator. The system itself incorporates a second-order oscillatory dynamic actuator, with an unknown nonlinear input-output relationship. The proposed algorithm not only accommodates the deadzone constraints on control inputs but also considers the actuator's saturation limits in control input calculations. It introduces a trajectory tracking mechanism that, instead of directly following the primary trajectory, adheres to an alternative trajectory capable of stable tracking, gradually converging to the main trajectory while accounting for operational constraints. In practical control systems, the actuator's input-output relationship is often nonlinear and unknown, requiring inversion for model-based control. This paper employs an offline-trained neural network trained on synthetic data to identify and approximate the actuator's behavior. To optimize the control system's performance and ensure stability during sudden error changes, the control input operates in two modes: position and velocity control. This dual-mode control allows for continuous switching between the two, facilitated by an innovative optimization technique based on the gradient descent method with a variable step size. Simulation results validate the effectiveness of the proposed algorithm in controlling systems constrained by hard limits and featuring nonlinear oscillatory actuators, providing a valuable contribution to the field of control systems.

Iterative Rule Extension for Logic Analysis of Data: An MILP-Based Heuristic to Derive Interpretable Binary Classifiers from Large Data Sets

Data-driven decision making is rapidly gaining popularity, fueled by the ever-increasing amounts of available data and encouraged by the development of models that can identify nonlinear input–output relationships. Simultaneously, the need for interpretable prediction and classification methods is increasing as this improves both our trust in these models and the amount of information we can abstract from data. An important aspect of this interpretability is to obtain insight in the sensitivity–specificity trade-off constituted by multiple plausible input–output relationships. These are often shown in a receiver operating characteristic curve. These developments combined lead to the need for a method that can identify complex yet interpretable input–output relationships from large data, that is, data containing large numbers of samples and features. Boolean phrases in disjunctive normal form (DNF) are highly suitable for explaining nonlinear input–output relationships in a comprehensible way. Mixed integer linear programming can be used to obtain these Boolean phrases from binary data though its computational complexity prohibits the analysis of large data sets. This work presents IRELAND, an algorithm that allows for abstracting Boolean phrases in DNF from data with up to 10,000 samples and features. The results show that, for large data sets, IRELAND outperforms the current state of the art in terms of prediction accuracy. Additionally, by construction, IRELAND allows for an efficient computation of the sensitivity–specificity trade-off curve, allowing for further understanding of the underlying input–output relationship. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms–Discrete. Funding: This work was supported by the Netherlands Organization for Scientific Research (Nederlandse Organisatie voor Wetenschappelijk Onderzoek) [Grant VI.VENI.192.043]. Supplemental Material: The online supplement is available at https://doi.org/10.1287/ijoc.2021.0284 .

Machine Learning Methods to Increase the Energy Efficiency of Buildings

Predicting a building’s energy consumption plays an important role as it can help assess its energy efficiency, identify and diagnose energy system faults, and reduce costs and improve climate impact. An analysis of current research in the field of ensuring the energy efficiency of buildings, in particular, their energy assessment, considering the types of models under consideration, was carried out. The principles, advantages, limitations, and practical application of the main data-based models are considered in detail, and priority future directions for forecasting the energy efficiency of buildings are highlighted. It is shown that the effectiveness of the methods is different for the main types of models and depends on the following factors: input data and parameters, the type and quality of available data for training, the suitability of the method for a specific type of model, etc. The need to consider the element of uncertainty when forecasting energy consumption due to the impossibility of accurate modeling of meteorological factors and the behavior of residents is emphasized. Therefore, machine learning methods, particularly deep learning-based models, are chosen to represent complex nonlinear input-output relationships, as they show higher performance than statistical time series forecasting methods. The analysis of published works revealed a lack of works describing a comprehensive energy forecasting information system for use in commercial projects. We proposed a new approach to combining semantic modeling and machine learning technologies for the energy management system of smart buildings, using the knowledge system of the semantic model we developed.

A Study on the Harmonic Distortion of Seismic-Grade Sigma-Delta MEMS Accelerometers Using a Multiple Degree-of-Freedom Model.

Harmonic distortion is one of the dominant factors limiting the overall signal-to-noise and distortion ratio of seismic-grade sigma-delta MEMS accelerometers. This study investigates harmonic distortion based on the multiple degree-of-freedom model (MDM) established in our previous study. The main advantage of using an MDM is that the effect of finger flexibility on harmonic distortion is considered. Initially, the nonlinear relationship between the input acceleration and output signal is derived using the MDM. Then, harmonic distortion is simulated and described in terms of the nonlinear input-output relationship. It is found that finger flexibility and parasitic capacitance mismatch both decrease harmonic distortion. Finally, the experimental testing of harmonic distortion is implemented. By reducing the finger length to realize a higher stiffness and compensating for the parasitic capacitance mismatch, the total harmonic distortion decreases from -66.8 dB to -86.9 dB.

Multi-Objective Optimization of The Low-Pressure Casting of Large-Size Aluminum Alloy Wheels through a Systematic Optimization Idea.

The process parameters in the low-pressure casting of large-size aluminum alloy wheels are systematically optimized in this work using numerical casting simulation, response surface methodology (RSM), and genetic algorithm (NSGA-II). A nonlinear input-output relationship was established based on the Box-Behnken experimental design (BBD) for the crucial casting parameters (pouring temperature, mold temperature, holding pressure, holding time), and response indicators (defect volume fraction, spokes large plane mean secondary dendrite spacing (SDAS)), and a mathematical model was developed by regression analysis. The Isight 2017 Design Gateway and NSGA-II algorithm were used to increase the population and look for the best overall solution for the casting parameters. The significance and predictive power of the model were assessed using ANOVA. Casting numerical simulation was used to confirm the best option. To accomplish systematic optimization in its low-pressure casting process, the mold cooling process parameters were adjusted following the local solidification rate. The results showed that the mathematical model was reliable. The optimal solutions were a pouring temperature of 703 °C, mold temperature of 409 °C, holding pressure of 1086 mb, and holding time of 249 s. The mold cooling process was further optimized, and the sequence solidification of the optimal solution was realized under the optimized cooling process. Finally, the wheel hub was manufactured on a trial basis. The X-ray detection, mechanical property analysis, and metallographic observation showed that the wheel hub had no X-ray defects and its mechanical properties were well strengthened. The effectiveness of the system optimization process scheme was verified.

Machine learning-based predictive control using on-line model linearization: Application to an experimental electrochemical reactor

The electrochemical reaction-based process, a new type of chemical process that can generate valuable products using renewable electricity, is a sustainable alternative to the traditional chemical manufacturing processes. One promising research area of electrochemical reaction processing is to reduce carbon dioxide (CO2) into carbon-based products, which can contribute to closing the carbon cycle if CO2 is directly captured from the atmosphere. In this work, we demonstrate a model predictive control (MPC) scheme that uses a neural network (NN) model as the process model to implement real-time multi-input-multi-output (MIMO) control in an electrochemical reactor for CO2 reduction. Specifically, a long short-term memory network (LSTM) model is developed using historical experimental data of the electrochemical reactor to capture the nonlinear input-output relationship as an alternative to the complex, first principles-based model. Furthermore, the Koopman operator method is used to linearize the LSTM model to reduce the nonlinear optimization step in the MPC to a well-understood and easy-to-solve quadratic programming (QP) problem. The performance of the LSTM model, Koopman-based optimization, and MPC using the linearization of the LSTM model are evaluated with various simulations as well as open-loop and closed-loop experiments. As the results, the proposed MPC scheme can drive the two output states, that are concentrations of the products (C2H4 and CO), to their desired setpoints by computing optimal input variables (surface potential and electrode rotation speed) in real-time in closed-loop experiments. Furthermore, a transfer learning-based method is utilized to update the NN model to handle process variability.

Soft-Computing-Based Estimation of a Static Load for an Overhead Crane.

Payload weight detection plays an important role in condition monitoring and automation of cranes. Crane cells and scales are commonly used in industrial practice; however, when their installation to the hoisting equipment is not possible or costly, an alternative solution is to derive information about the load weight indirectly from other sensors. In this paper, a static payload weight is estimated based on the local strain of a crane's girder and the current position of the trolley. Soft-computing-based techniques are used to derive a nonlinear input-output relationship between the measured signals and the estimated payload mass. Data-driven identification is performed using a novel variant of genetic programming named grammar-guided genetic programming with sparse regression, multi-gene genetic programming, and subtractive fuzzy clustering method combined with the least squares algorithm on experimental data obtained from a laboratory overhead crane. A comparative analysis of the methods showed that multi-gene genetic programming and grammar-guided genetic programming with sparse regression performed similarly in terms of accuracy and both performed better than subtractive fuzzy clustering. The novel approach was able to find a more parsimonious model with its direct implantation having a lower execution time.

Observer-Based Robust Adaptive TS Fuzzy Control of Uncertain Systems with High-Order Input Derivatives and Nonlinear Input–Output Relationships

Observer-Based Robust Adaptive TS Fuzzy Control of Uncertain Systems with High-Order Input Derivatives and Nonlinear Input–Output Relationships

Towards single atom computing via high harmonic generation

The development of alternative platforms for computing has been a longstanding goal for physics, and represents a particularly pressing concern as conventional transistors approach the limit of miniaturization. A potential alternative paradigm is that of reservoir computing, which leverages unknown, but highly nonlinear transformations of input-data to perform computations. This has the advantage that many physical systems exhibit precisely the type of nonlinear input-output relationships necessary for them to function as reservoirs. Consequently, the quantum effects which obstruct the further development of silicon electronics become an advantage for a reservoir computer. Here we demonstrate that even the most basic constituents of matter–atoms–can act as a reservoir for computing where all input-output processing is optical, thanks to the phenomenon of High Harmonic Generation. A prototype single-atom computer for classification problems is proposed, where a classification model is mapped to an all-optical setup, with linear filters chosen to correspond to the trained model’s parameters. We numerically demonstrate that this ‘all-optical’ computer can successfully perform classification tasks, and does so with an accuracy that is strongly dependent on dynamical nonlinearities. This may pave the way for the development of petahertz information processing platforms.

Algorithm and Architecture Design of Random Fourier Features-Based Kernel Adaptive Filters

Numerous real-life systems exhibit complex nonlinear input-output relationships. Kernel adaptive filters, a popular class of nonlinear adaptive filters, can efficiently model these nonlinear input-output relationships. Their growing network structure, however, poses considerable challenges in terms of their hardware implementation, making them inefficient for real-time applications. Random Fourier features (RFF) facilitate the development of kernel adaptive filters with a fixed network structure. For the first time, this paper attempts to implement the RFF-based kernel least mean square (RFF-KLMS) algorithm on hardware. To this end, we propose several reformulations of the feature functions (FFs) that are computationally expensive in their native form so that they can be implemented in real-time VLSI. Specifically, we reformulate inner product evaluation, cosine, and exponential functions that appear in the implementation of FFs. With these reformulations, the proposed delayed RFF-KLMS (DRFF-KLMS) is then synthesized using 45-nm CMOS technology with 16-bit fixed-point representations. According to the synthesis results, pipelined DRFF-KLMS architectures require minimal hardware increase over the state-of-the-art conventional delayed LMS architecture while significantly improving estimation performance for the nonlinear model. Our results suggest that the cosine feature function-based DRFF-KLMS is appropriate for applications requiring high accuracy, whereas the exponential function-based DRFF-KLMS may be well suited for resource-constrained applications.

A spatio-temporal nonlinear semi-analytical framework describing longitudinal waves propagation in damaged structures based on Green–Volterra formalism

Structural Health Monitoring (SHM) of aeronautic structures by means of Lamb waves opens promising perspectives in terms of maintenance costs reduction and safety increases. Lamb waves interactions with damages are known to be nonlinear, a property still largely underexploited in SHM. Difficulties in this context are (i) to be able to distinguish between nonlinearities due to the waves spatial propagation (i.e. material or geometrical nonlinearities) and those located at the damage position, (ii) to handle computational complexity associated with spatio-temporal nonlinear models, and (iii) to be able to physically link recorded signals with actual damage state. This work proposes to rely on the Green–Volterra formalism to build up a semi-analytical spatio-temporal framework describing longitudinal waves propagation and damage interaction able to physically represent both types of nonlinearities, and computationally simple enough to be tractable in real-time for SHM purposes. This approach is detailed here for longitudinal waves, which corresponds in the low frequency × thickness range to the S0 Lamb wave mode propagating in a damaged beam. A spatio-temporal semi-analytical model of the nonlinear longitudinal waves propagation is first derived, where the damage is represented by a polynomial stiffness characteristic acting via boundary conditions at a given position in the beam. This model is then used to derive the Green–Volterra series describing the nonlinear input–output relationship of the system. A modal decomposition of the Green–Volterra series is also provided to ease implementation and reduce computational cost. The proposed spatio-temporal semi-analytical approach is then successfully compared to state-of-the-art nonlinear Lamb waves simulation methods based on finite-element models. It is finally shown on a simulated example and discussed in detail how such a nonlinear framework could potentially be relevant for SHM purposes.

Global Incremental Flight Control for Agile Maneuvering of a Tailsitter Flying Wing

This paper proposes a novel control law for accurate tracking of agile trajectories using a tailsitter flying wing unmanned aerial vehicle that transitions between vertical takeoff and landing and forward flight. The global control formulation enables maneuvering throughout the flight envelope, including uncoordinated flight with sideslip. Differential flatness of the nonlinear tailsitter dynamics with a simplified aerodynamics model is shown. Using the flatness transform, the proposed controller incorporates tracking of the position reference along with its derivatives velocity, acceleration, and jerk, as well as the yaw reference and yaw rate. The inclusion of jerk and yaw rate references through an angular velocity feedforward term improves tracking of trajectories with fast-changing accelerations. The controller does not depend on extensive aerodynamic modeling but instead uses incremental nonlinear dynamic inversion to compute control updates based on only a local input–output relation, resulting in robustness against discrepancies in the simplified aerodynamics equations. Exact inversion of the nonlinear input–output relation is achieved through the derived flatness transform. The resulting control algorithm is extensively evaluated in flight tests, where it demonstrates accurate trajectory tracking and challenging agile maneuvers, such as sideways flight and aggressive transitions while turning.

Adaptive Weighted Neighbors Method for Sensitivity Analysis.

Identifying key factors from observational data is important for understanding complex phenomena in many disciplines, including biomedical sciences and biology. However, there are still some limitations in practical applications, such as severely nonlinear input-output relationships and highly skewed output distributions. To acquire more reliable sensitivity analysis (SA) results in these extreme cases, inspired by the weighted k-nearest neighbors algorithm, we propose a new method called adaptive weighted neighbors (AWN). AWN makes full use of the information contained in all training samples instead of limited samples and automatically gives more weight to nearby samples. Then, the bootstrap technique and Jansen's method are used to obtain reliable SA results based on AWN. We demonstrate the performance and accuracy of AWN by analyzing various biological and biomedical data sets, three simulated examples and two case studies, showing that it can effectively overcome the above limitations. We therefore expect it to be a complementary approach for SA.

Fault prediction of combine harvesters based on stacked denoising autoencoders

Accurate fault prediction is essential to ensure the safety and reliability of combine harvester operation. In this study, a combine harvester fault prediction method based on a combination of stacked denoising autoencoders (SDAE) and multi-classification support vector machines (SVM) is proposed to predict combine harvester faults by extracting operational features of key combine components. In general, SDAE contains autoencoders and uses a deep network architecture to learn complex non-linear input-output relationships in a hierarchical manner. Selected features are fed into the SDAE network, deep-level features of the input parameters are extracted by SDAE, and an SVM classifier is then added to its top layer to achieve combine harvester fault prediction. The experimental results show that the method can achieve accurate and efficient combine harvester fault prediction. In particular, the experiments uses Gaussian noise with a distribution center of 0.05 to corrupt the test data samples obtained by random sampling of the whole population, and the results showed that the prediction accuracy of the method is 95.31%, which has better robustness and generalization ability compared to SVM (77.03%), BP (74.61%), and SAE (90.86%). Keywords: fault prediction, combine harvester, stacked denoising autoencoders, support vector machines DOI: 10.25165/j.ijabe.20221502.6963 Citation: Qiu Z M, Shi G X, Zhao B, Jin X, Zhou L M, Ma T F. Fault prediction of combine harvesters based on stacked denoising autoencoders. Int J Agric & Biol Eng, 2022; 15(2): 189–196.

Looking at the bigger PICture: understanding and counteracting the decline of persistent inward currents in older adults.

Looking at the bigger PICture: understanding and counteracting the decline of persistent inward currents in older adults.

Non-Linear Visualization and Importance Ratio Analysis of Multivariate Polynomial Regression Ecological Models Based on River Hydromorphology and Water Quality

Multivariate polynomial regression (MPR) models were developed for five macrophyte indices. MPR models are able to capture complex interactions in the data while being tractable and transparent for further analysis. The performance of the MPR modeling approach was compared to previous work using artificial neural networks. The data were obtained from hydromorphologically modified Polish rivers with a widely varying water quality. The modeled indices were the Macrophyte Index for Rivers (MIR), the Macrophyte Biological Index for Rivers (IBMR), and the River Macrophyte Nutrient Index (RMNI). These indices measure the trophic and ecological status of the rivers. Additionally, two biological diversity indices, species richness (N) and the Simpson index (D), were modeled. The explanatory variables were physico-chemical properties depicting water quality and river hydromorphological status indices. In comparison to artificial neural networks, the MPR models performed similarly in terms of goodness of fit. However, the MPR models had advantages such as model simplicity and ability to be subject to effective visualization of complex nonlinear input–output relationships, as well as facilitating sensitivity analysis using importance ratios to identify effects of individual input variables.

Mapping dependencies of BOLD signal change to end-tidal CO2: Linear and nonlinear modeling, and effect of physiological noise correction

BackgroundDisentangling physiological noise and signal of interest is a major issue when evaluating BOLD-signal changes in response to breath holding. Currently-adopted approaches for retrospective noise correction are general-purpose, and have non-negligible effects in studies on hypercapnic challenges. New methodWe provide a novel approach to the analysis of specific and non-specific BOLD-signal changes related to end-tidal CO2 (PETCO2) in breath-hold fMRI studies. Multiple-order nonlinear predictors for PETCO2 model a region-dependent nonlinear input-output relationship hypothesized in literature and possibly playing a crucial role in disentangling noise. We explore Retrospective Image-based Correction (RETROICOR) effects on the estimated BOLD response, applying our analysis both with and without RETROICOR and analyzing the linear and non-linear correlation between PETCO2 and RETROICOR regressors. ResultsThe RETROICOR model of noise related to respiratory activity correlated with PETCO2 both linearly and non-linearly. The correction affected the shape of the estimated BOLD response to hypercapnia but allowed to discard spurious activity in ventricles and white matter. Activation clusters were best detected using non-linear components in the BOLD response model. Comparison with existing methodWe evaluated the side-effects of standard physiological noise correction procedure, tailoring our analysis on challenging understudied brainstem and subcortical regions. Our novel approach allowed to characterize delays and non-linearities in BOLD response. ConclusionsRETROICOR successfully avoided false positives, still broadly affecting the estimated non-linear BOLD responses. Non-linearities in the model better explained CO2-related BOLD signal fluctuations. The necessity to modify the standard procedure for physiological-noise correction in breath-hold studies was addressed, stating its crucial importance.

A data-driven model for nonlinear marine dynamics

The design and engineering of ships and platforms that operate in the ocean environment requires understanding of a nonlinear dynamical system that responds according to complex interaction with a wide range of sea and wind conditions. Time domain observation of nonlinear marine dynamics with either experiments or high-fidelity numerical simulation tools is costly due to the random nature of the ocean and the full range of environmental and loading conditions that are experienced in the lifetime of a ship or platform. In this paper, a data-driven method is presented to predict the complex nonlinear input–output relationship typical of marine systems. A Long Short-Term Memory neural net is used to learn nonlinear wave propagation and the nonlinear roll of a ship section in beam seas. Training data are generated with second-order wave theory or a volume-of-fluid computational fluid dynamics, although the method is directly applicable to data that is generated by other means such as nonlinear potential flow or experimental measurements. The cost and the amount of data to apply the method are estimated and measured. The data-driven results are compared with unseen data to demonstrate the accuracy and feasibility.

Hybrid multi-task learning-based response surface modeling in manufacturing

Response surface modeling is an essential technique for identifying the optimal input parameters in a process, especially when the physical knowledge about the process is limited. It explores the relationships between the process input variables and the response variables through a sequence of designed experiments. Conventional response surface models typically rely on a large number of experiments to achieve reliable modeling performance, which can be cost prohibitive and time-consuming. Furthermore, nonlinear input-output relationships in some processes may not be sufficiently accounted for by existing modeling methods. To address these challenges, this paper develops a new response surface modeling approach based on hybrid multi-task learning (H-MTL). This approach decomposes the variability in process responses into two components–a global trend and a residual term, which are estimated through self-learning and MTL of Gaussian process (GP), respectively. MTL leverages the similarities between multiple similar-but-not-identical GPs, thus achieving superior modeling performance without increasing experimental cost. The effectiveness of the proposed method is demonstrated by a case study using experimental data collected from real-world ultrasonic metal welding processes with different material combinations. In addition, the hyperparameter selection, the effects of the number of tasks, and the determination of the stopping criterion are discussed in detail.