Modal Transformation Research Articles

Load-independent multi-objective sensor placement method for localization and reconstruction of external excitations under interval uncertainties

The direct measurement of external excitations under operation conditions remains challenging in many engineering applications. This study proposes a method of optimal sensor placement for the best localization and reconstruction of external excitations when considering multi-source uncertainties. The excitation inversion is achieved in the framework of minimizing the discrepancy between the forward and inversed modal loads. To accurately obtain the modal force in the time-domain excitation reconstruction algorithm, three combined indicators of the interested modal matrix are defined, which integrate measures of effectiveness, stability, orthogonality, and robustness of inverse modal transformation. The optimal sensor placement is determined by multi-objective particle swarm optimization and Pareto optimal solution. In addition, to alleviate the computational burden of loading localization, a surrogate model based on an interval kriging interpolation model and sequential sampling strategies is established for the forward modal forces. And a time-dependent interval error of modal forces inspired by the theory of second-order narrow bounds in system reliability is developed to guide the inversion process. Notably, the developed sensor selection and excitation inversion methods are independent of the type, location, and time evolution of external excitations. Eventually, two numerical examples and an experimental case are discussed to demonstrate the validity and feasibility of the developed approach.

Dynamic Stability Analysis of Square Isotropic/Laminated Composite Plates With Circular Cutout Subjected to Non-Uniform Follower Edge Load With Damping

The present investigation deals with the study of vibration and dynamic instability behaviour of square isotropic/laminated composite plates with circular hole subjected to partially distributed follower edge forces using finite element method. The first order shear deformation theory is used to model the plate, considering the effects of shear deformation and rotary inertia. The modal transformation technique is applied to the resulting equilibrium equation for subsequent analysis. Structural damping is introduced into the system in terms of equivalent viscous damping to study the significance of damping on stability characteristics. The effects of cutout size, load width, boundary condition, ply orientation, direction control of the load and damping parameters are considered for the stability behaviour of the plates. The results show that under follower loading, the system is susceptible to instability due to flutter alone or due to both flutter and divergence, depending on system parameters.

Multi-type dynamic load identification algorithm in continuous system: A numerical and experimental study based on SSM-Newmark-β

Dynamic load identification based on structural responses is an important problem in the field of engineering and plays an important role in the condition assessment of mechanical structures. Current popular load identification methods such as the state-space method (SSM) and the Green's kernel function method (GKFM) are implemented on discrete systems with outstanding performance, but when dealing with complex continuous systems, there are some limitations such as low efficiency and inaccuracy. In this paper, a continuous system load identification algorithm based on SSM and Newmark-β is proposed for the first time. Using modal coordinate transformation and modal truncation methods, the number of infinite vibration differential equations of a continuous system in physical space are converted to a finite number of vibration differential equations in modal space, where the modal truncation order and the optimal layout of the sensors are combined by modal strain energy. The Newmark-β method in modal space is derived and thus combined with SSM to obtain a load identification model Y=HF called SSM-Newmark-β method, which reduces the size of the transfer matrix H. The solution time of the proposed algorithm is 0.38 s for continuous systems, which is rather shorter than that for discrete systems. Furthermore, the simulations show that it has better accuracy and noise immunity than SSM and GKFM in the identification of sinusoidal load, impact load, and random load. The effect of time step is also discussed which reveals that the larger time step has less effect on the proposed algorithm. An experimental study is carried out on a cantilever beam system. The result verifies that the SSM-Newmark-β algorithm has better accuracy in load identification for the continuous system. This research provides a new sight for the real-time identification of dynamic loads for complex structures.

Modal Transformation based Fault Location in Radial Distribution Network

This paper introduces the technique of fault distance estimation based on modal transformation and signal processing. The recorded faulted phase currents are applied to the Karrenbauer model transformation and these model component currents are decomposed into detail coefficients by the use of Daubechies wavelet, db6. The fault recorder installed at the terminal of the feeder records different time delays between the modal components. In order to find fault distance, the time delay values and modal components velocity are used in traveling wave theory. This paper compares two different conditions: the first condition does not use a modal transformation and the second condition uses a modal transformation. When using modal transformation conditions, three different coefficient levels (detail coefficient level 1 (D1); the combination of detail coefficient level 1+2 (D1+2) and the combination of detail coefficient level 1+2+3 (D1+2+3) ) are used to estimate the fault distance. Different fault types with different fault locations are created in MATLAB simulation.

Multi-Modal and Self-Reconstruction Conditioning Circuit of Semiconductor Gas Sensors

Semiconductor gas sensors (chemiresistors) have been widely used in many fields. The emerging novel gas sensors usually have large initial resistance and ultra-high sensitivity, and their resistance value may change significantly during the response process. It is difficult for conventional front-end conditioning circuits to meet the requirements of large measurement range and high accuracy. Meanwhile, the circuit needs to be compatible with several forms of signals generated from different types of sensors, such as voltage, current, and resistance. This study designs a front-end conditioning circuit that is compatible with various types of gas sensors and can adjust the measurement range in real time. The circuit has different functional states, which can realize four functions: constant voltage measurement, constant current measurement, electrochemical measurement, and parameter calibration. The modal transformation of the circuit is controlled by a multiplexer, which can perform automatic transformation according to software instructions. Our work provides a flexible circuit framework composed of different functional units, with the characteristics of multi-modal and self-reconstruction. It is suitable for designing integrated or fixed-function circuits and is convenient for miniaturization and cost reduction.

A study on data-driven identification and representation of nonlinear dynamical systems with a physics-integrated deep learning approach: Koopman operators and nonlinear normal modes

Identifying the intrinsic coordinates or modes of dynamical systems is essential to understand, analyze, and characterize the underlying complex dynamical behaviors. This is a critical challenge for nonlinear dynamical systems because the modal transformation, which is universal for linear systems, no longer applies. Koopman operators and nonlinear normal modes (NNMs) are two main frameworks aiming to provide a general representation of nonlinear dynamics. In this study, we investigate their abilities on representing nonlinear dynamical systems. Addressing the challenge that the closed-form models or equations of dynamical systems are generally unknown realistically, we first present a physics-integrated deep learning-based data-driven framework to identify the eigenfunction of Koopman operators and the nonlinear modal transformation function of NNMs, respectively. We then evaluate their representation abilities by their reconstruction and predictive accuracy of the nonlinear dynamical response using the identified Koopman modes and NNMs. We conduct numerical experiments on Duffing systems with varying nonlinearity levels and dimensions, and observe that NNMs achieve higher representation accuracy and better computational efficiency than Koopman operators using the same dimension of intrinsic coordinates or modes.

Damping of Inter-Area Oscillations Using TCPS Based Delay Compensated Robust WADC

Low-frequency oscillations (LFOs) pose a significant obstacle in achieving optimal power flow and utilizing transmission corridors in large interconnected power systems. In this study, linear matrix inequality (LMI) base robust wide-area damping controller (WADC) is introduced to effectively address critical LFOs. The proposed WADC utilizes wide-area signals, which modulate the phase angle of a thyristor-controlled phase shifter device. To ensure that the concerned modes of LFOs lie in left half of the complex plane, a D-space sub-region approach is applied. However, using wide-area signals introduces time delays, which negatively impact the efficacy of the WADC; hence, a time delay compensator (TDC) is incorporated into the feedback path of the signals. The proposed approach involves four key steps: selecting feedback signals using a combined modal transformation and geometric approach, designing an appropriate TDC, building a generalized plant with mixed sensitivity weights, and solving the LMI. The dynamic efficacy is verified on IEEE 4-machine 11-bus system, and 10-machine 39-bus system. Poorly damped single and multiple critical modes are placed in the D-space region of interest with specified damping ratios viz. 10% and 15%. Furthermore, damping ratios of critical modes are maintained with TDC based proposed WADC while deteriorating with other counterparts.

Field coupling-induced synchronization of a functional neuron with magnetic field perception

It is difficult to explore the induced mechanism of neuronal firing activity and the cooperation between neurons experimentally, so some neuronal circuits are established to train mode transformation and selection. Furthermore, some functional device, for example, piezoelectric ceramic, thermistor, phototube are inset in neuronal circuits and the functional neurons are developed to perceive some specific physical signal. In this paper, a linear resistance and an ideal Josephson junction are parallelly connected to FitzHugh-Nagumo (FHN) neuronal circuit, and then a functional neuron is established to percept the induction currents induced by the external magnetic field. Some basic dynamics are analyzed in terms of two-parameter bifurcation, one-parameter bifurcation and interspike interval(ISI for short) bifurcation, it is indicated that the functional neuron is sensitive to the electromagnetic stimulation and has rich multimodal transformations. The period-adding bifurcations accompanied by multi-period and chaos between two period cascades occupy the entire bifurcation interval when the external magnetic field is given in steady state, while the irregular modal transformations between period and chaos can be observed when the functional neuron encounters a periodic external magnetic field. Furthermore, two functional neurons are bridged with a capacitor, so field coupling is induced, then the effects of coupling strengths on complete synchronization are investigated by calculating the synchronization error function and the bifurcation diagram. In addition, the local dynamics of the network node play an important role in collective behavior and synchronous transition, so two capacitor-coupled functional neurons is presented as the network nodes, and a chain neural network is constructed to explore the effects of external magnetic field and coupling strength on network synchronous behavior. Obviously, the orderliness of the neural network can enhance or destroy under different modulation of external magnetic stimulation and coupling strength. It can give insights to investigate synchronization on neural networks with field coupling and useful guidance for implementing artificial synapse for signal processing.

Modal Space Control of Bilateral System with Elasticity for Stable Contact Motion

Bilateral control realizes position synchronization and the “law of action and reaction” between two points. To advance applications of bilateral control, it is necessary to emphasize environmental adaptability, safety, and task execution. Accordingly, the bilateral system is required to consider contact with unknown environments and realize stable contact to avoid harm to the operator or the object. Thus, a bilateral control system using elastic manipulators is proposed in this paper. Moreover, the integration of mechanical and control designs for stable interaction with the operator and the environment is discussed. The proposed bilateral system with elasticity is modeled as a pair of two-mass resonant systems. Accordingly, a modal space control (MSC) is introduced with the aim of realizing the control goals, vibration suppression, and good operationality. Modal transformation independently configures the force and position controllers of each other in virtual common and differential spaces. MSC comprises reaction torque feedback loops in the modal space and modal space load-side disturbance observer (MLOB). MLOB compensates for load-side disturbance, including the interference between the common and the differential modes. It realizes disturbance suppression, decoupling control, and nominalization of parameters in the form suitable for each force and position control system.

Interpolation‐based parametric model order reduction of automotive brake systems for frequency‐domain analyses

Brake squeal describes noise with different frequencies that can be emitted during the braking process. Typically, the frequencies are in the range of 1 to 16 kHz. Although the noise has virtually no effect on braking performance, strong attempts are made to identify and eliminate the noise as it can be very unpleasant and annoying. In the field of numerical simulation, the brake is typically modeled using the Finite Element method, and this results in a high-dimensional equation of motion. For the analysis of brake squeal, gyroscopic and circulatory effects, as well as damping and friction, must be considered correctly. For the subsequent analysis, the high-dimensional damped nonlinear equation system is linearized. This results in terms that are non-symmetric and dependent on the rotational frequency of the brake rotor. Many parameter points to be evaluated implies many evaluations to determine the relevant parameters of the unstable system. In order to increase the efficiency of the process, the system is typically reduced with a truncated modal transformation. However, with this method the damping and the velocity-dependent terms, which have a significant influence on the system, are neglected for the calculation of the eigenmodes, and this can lead to inaccurate reduced models. In this paper, we present results of other methods of model order reduction applied on an industrial high-dimensional brake model. Using moment matching methods combined with parametric model order reduction, both the damping and the various parameter-dependent terms of the brake model can be taken into account in the reduction step. Thus, better results in the frequency domain can be obtained. On the one hand, as usual in brake analysis, the complex eigenvalues are evaluated, but on the other hand also the transfer behavior in terms of the frequency response. In each case, the classical and the new reduction method are compared with each other.

A Categorical Normalization Proof for the Modal Lambda-Calculus

We investigate a simply typed modal $\lambda$-calculus, $\lambda^{\to\square}$, due to Pfenning, Wong and Davies, where we define a well-typed term with respect to a context stack that captures the possible world semantics in a syntactic way. It provides logical foundation for multi-staged meta-programming. Our main contribution in this paper is a normalization by evaluation (NbE) algorithm for $\lambda^{\to\square}$ which we prove sound and complete. The NbE algorithm is a moderate extension to the standard presheaf model of simply typed $\lambda$-calculus. However, central to the model construction and the NbE algorithm is the observation of Kripke-style substitutions on context stacks which brings together two previously separate concepts, structural modal transformations on context stacks and substitutions for individual assumptions. Moreover, Kripke-style substitutions allow us to give a formulation for contextual types, which can represent open code in a meta-programming setting. Our work lays the foundation for extending the logical foundation by Pfenning, Wong, and Davies towards building a practical, dependently typed foundation for meta-programming.

A Two-Step Approach for the Analysis of Bulk Current Injection Setups Involving Multiwire Bundles

In this work, a two-step procedure to predict maximum (worst-case scenario) and minimum (best-case scenario) noise levels induced by bulk current injection (BCI) at the terminal sections of a wiring harness is presented. To this end, common mode (CM) and differential mode (DM) quantities are introduced by a suitable modal transformation, and equivalent modal circuits are derived, where CM (dominant mode) into DM (secondary mode) conversion is modelled by induced sources included into the DM circuit. The procedure initially foresees the solution of the CM circuit to provide input data for subsequent solution of the DM circuit. Such a two-step approach is then used to develop a probabilistic–possibilistic framework for computationally-efficient estimation of lower and upper boundaries to the variability of the noise voltages induced at the bundle terminations. To this end, random uncertainty affecting certain setup parameters is addressed through probability theory, whereas epistemic uncertainty is represented via possibility theory. Accuracy and computational efficiency of the proposed two-step method are assessed by examples involving seven and nineteen wire harnesses.

A Survey on Learning Objects' Relationship for Image Captioning.

Image captioning is a challenging modality transformation task in computer vision and natural language processing, aiming to understand the image content and describe it with a natural language. Recently, the relationship information between objects in the image has been investigated to be of importance in generating a more vivid and readable sentence. Many types of research have been done in relationship mining and learning for leveraging into the caption models. This paper mainly summarizes the methods of relational representation and relational encoding in image captioning. Besides, we discuss the advantages and disadvantages of these methods and provide commonly used datasets for the relational captioning task. Finally, the current problems and challenges in this task are highlighted.

Implementation of an Alternative Frequency-Dependent Three-Phase Transmission Line Model Based on the Folded Line Equivalent Model in MatLab-Simulink

This paper proposes an alternative multiconductor transmission line model that combines the folded line equivalent with the modal transformation. The folded line equivalent decomposes the nodal admittance matrix of a transmission line into its open-circuit and short-circuit contributions. These contributions are fitted to rational functions, which are associated with Norton equivalent circuits based on their state space models. The proposed model uses an orthogonal matrix to transform voltages and currents from the phase domain to the folded line equivalent domain and vice versa. Because the transformation matrix is orthogonal, we represent it using ideal transformers in simulation software. First, we use a circuit representation of Clarke’s matrix to decompose a transmission line into its modes. Then, each mode is decomposed into its open-circuit and short-circuit contributions using a circuit implementation of the proposed matrix. The proposed approach can accurately represent short lines in simulations with time steps equal to or greater than the propagation time of the transmission line. We compare the results obtained with the proposed approach to those obtained with power systems computer-aided design/electromagnetic transients including the DC universal line model.

Physics-constrained deep learning of nonlinear normal modes of spatiotemporal fluid flow dynamics

In this study, we present a physics-constrained deep learning method to discover and visualize from data the invariant nonlinear normal modes (NNMs) which contain the spatiotemporal dynamics of the fluid flow potentially containing strong nonlinearity. Specifically, we develop a NNM-physics-constrained convolutional autoencoder (NNM-CNN-AE) integrated with a multi-temporal-step dynamics prediction block to learn the nonlinear modal transformation, the NNMs containing the spatiotemporal dynamics of the flow, and reduced-order reconstruction and long-time future-state prediction of the flow fields, simultaneously. In test cases, we apply the developed method to analyze different flow regimes past a cylinder, including laminar flows with low Reynolds number in transient and steady states (RD = 100) and high Reynolds number flow (RD = 1000), respectively. The results indicate that the identified NNMs are able to reveal the nonlinear spatiotemporal dynamics of these flows, and the NNMs-based reduced-order modeling consistently achieves better accuracy with orders of magnitudes smaller errors in construction and prediction of the nonlinear velocity and vorticity fields, compared to the linear proper orthogonal decomposition (POD) method and the Koopman-constrained-CNN-AE using the same number or dimension of modes. We perform an analysis of the modal energy distribution of NNMs and find that compared to POD modes, the few fundamental NNMs capture a very high level of total energy of the flow, which is advantageous for reduced-order modeling and representation of the complex flows. Finally, we discuss the potentials and limitations of the presented method.

Study on the Influencing Factors of Modal Transformation of Continuous Rotating Detonation Wave Propagation

In order to study the propagation mode of rotating detonation wave, the detailed reaction mechanism of hydrogen-oxygen with 9 components and 19 steps is used, and the finite rate chemical reaction model is used for numerical calculation. After ignition, there is a stable collision period in the flow field for a certain period, and the collision extinguishing and new detonation wave generation occur during the mode conversion. By adding nitrogen or argon to the hydrogen-oxygen mixture for dilution, when the dilution ratio increases, the activity of the gas mixture decreases, the height of the combustible gas layer increases, and the temperature of the combustion product after the detonation wave decreases away from the head of the detonation wave, which will reduce the mixture that is burned in advance. There are different degrees of reflected shock at the outlet of the combustion chamber, and the upward detonation wave will cause the height change of the detonation wave head and the instability of the flow.

The law of blast stress wave propagation and fracture development in soft and hard composite rock

The process of blasting stress wave propagation and crack propagation is directly affected by the physical properties of the rock mass and internal joints in the rock. In soft and hard rock layers, the blasting process is more complicated since the blasting stress wave needs to penetrate two kinds of rocks with different physical properties and the interface between soft rock and hard rock. In this study, the modal transformation of stress waves at the interface of layered composite rock was analyzed, and the process was reproduced by finite element analysis. Furthermore, the development law of cracks was explored. The research results demonstrated that in the single blasting-hole model, a triangular crack area caused by reflected stress waves appeared at the rock interface of rock medium I near the blast hole. In rock medium II, the tensile crack generated by the interface wave appeared on the side away from the blast hole. Besides, the development of the tensile crack was associated with the incident mode of the blast stress wave and the incident angle. In the deep hole blasting model, the incidence of the detonation wave front from hard rock to soft rock promoted the fragmentation of the hard rock.

Improving multimodal fusion with Main Modal Transformer for emotion recognition in conversation

Emotion recognition in conversation (ERC) is essential for developing empathic conversation systems. In conversation, emotions can exist in multiple modalities, i.e., audio, text, and visual. Due to the inherent characteristics of each modality, it is not easy for the model to use all modalities effectively when fusing modal information. However, existing approaches consider the same representation ability of each modality, resulting in unsatisfactory fusion across modalities. Therefore, we consider different modalities with different representation abilities, propose the concept of the main modal, i.e., the modal with stronger representation ability after feature extraction, and then propose the method of Main Modal Transformer (MMTr) to improve the effect of multimodal fusion. The method preserves the integrity of the main modal features and enhances the representation of weak modalities by using multihead attention to learn the information interactions between modalities. In addition, we designed a new emotional cue extractor that extracts emotional cues from two levels (the speaker’s self-context and the contextual context in conversation) to enrich the conversation information obtained by each modal. Extensive experiments on two benchmark datasets validate the effectiveness and superiority of our model.

MODAL TRANSFORM FEATURES OF CABLE LINE ELECTRICAL VALUES IN A TRAVELING WAVE FAULT LOCATOR

It is known that during a short circuit on an overhead line, the traveling waves in the phases contain components of two aerial and one ground modes. Due to the different propagation velocity along the line of these components at the locator installation place they arrive at different times. This leads to the fact that the traveling wave front in the phases becomes less pronounced, and, consequently, the accuracy of determining their arrival time and accuracy of the fault location decrease. To divide the phase values ​​of an overhead line into independent components of modes, invariant transformations – Clark transformation, Karrenbauer transformation, or Wedepohl transformation – are used. However, these transformations in their classical form cannot be applied to the electrical values of a cable line, since its design differs from that of an overhead power line. The purpose of the article is to illustrate the use of modal transformation on a cable line. As a result of the study, the following conclusions were obtained: currents in the cable line cores do not affect each other, therefore, in the wave fault locator that measures current waves, it is necessary to use directly the phase currents of the cores without modal transformation; if the wave fault locator measures the currents or voltages of the cable screens, the modal transformation should be performed, and it must be taken into account that the three modes formed by the screens are similar to the three modes of the overhead line; if a power transformer is adjacent to the cable line, the current traveling waves in the cores will be completely reflected from the measurement place, in this case in the wave fault locator it is necessary to use voltage traveling waves in the mode between the core and the screen of each cable of the three-phase group.

Multimodal convolutional neural network model with information fusion for intelligent fault diagnosis in rotating machinery

Accurate and efficient fault diagnosis in rotating machinery has long been important and challenging, as it strongly affects the system reliability and safety of industrial applications. In recent years, deep-learning-based methods are developing rapidly and have been widely used in different areas. However, most of them are data-driven and focus on the architecture and design of convolutional neural network (CNN) models, while neglecting the representation of information itself. The intrinsic characteristics of the signal can not fully explored. Moreover, rich multidirectional information hidden inside the signal, which is the key to improving the predictive performance of the entire fault diagnosis model, has usually been ignored. In this work, we propose a multimodal neural-network-based model to pursue feature representation more efficiently and effectively and further improve the diagnostic performance. This method innovatively combines continuous wavelet transform and symmetrized dot pattern graphs through the channel information fusion mechanism after the two-dimensional domain modal transformation of the time-domain signal. The integration of one- and two-dimensional convolutions could fully utilize the feature extraction capability of CNN for multimodal signals, thus forming a multimodal CNN architecture under two-level information fusion. The experiment results prove that the designed model can achieve better performance than the traditional single-modal CNN structure.