Non-uniform System Research Articles

Research on a novel non-uniform and asymmetric ultrasonic vibration system

Abstract A new type of non-uniform and asymmetric ultrasonic vibration system is proposed and applied to the turning process. The research results show that the design theory of the non-uniform and non-symmetric ultrasonic vibration system is accurate and reliable.The theoretical design frequency and modal simulation frequency error of Ultrasonic Vibration Turning System (UVTS) is only 2.5%. The designed non-uniform and non-symmetric ultrasonic vibration system has excellent vibration performance and stability, and the established simulation model can predict surface microtexture accurately. The vibration mode output by the non-uniform and non-symmetric ultrasonic vibration system is longitudinal-bending vibration, and the actual vibration performance is excellent. Compared with conventional cutting, the addition of longitudinal-bending ultrasonic vibration under the same conditions can give the machined surface a microscopic textured structure, reduce surface roughness and water contact angle, and improve surface wettability.The minimum surface roughness obtained in the experiment is 1.005 μm.The orthogonal experiment results show that there is a correlation between the machining parameters, surface micro-structure parameters, surface wettability, and surface roughness.

Chemo-elasto-electro free energy of non-uniform system in the diffuse interface context

In the present work, we propose an alternative approach for deriving the free energy formulation of a non-uniform system. Compared with the work of Cahn and Hilliard (1958 J.Chem. Phys.28258-67), our approach provides a more comprehensive explanation for the individual energy contribution in a non-uniform system, including entropy, interaction energy, and internal energy. By employing a fundamental mathematical calculus, we reformulate the local composition within the interface region. Utilizing the reformulated local composition as well as classic thermodynamic principles, we establish formal expressions for entropy, interaction energy, and the internal energy, which are functions of both composition and composition gradients. We obtain a comprehensive free energy expression for a non-uniform system by integrating these energy density formulations. The obtained free energy expression is consistent with the formula type of Cahn and Hilliard and prodives more deeper physical interpretation. Moreover, using the same approach, we derive formulations for elastic energy and electric potential energy in a non-uniform system. However, the proposed approach encounters a limitation in the special case of a non-uniform fluid contacting a solid substrate. Due to the significant difference in the length scales between the solid-fluid and fluid-fluid interfaces, the wall free energy formulation based on the aforementioned concept is unsuitable for this multi-scale system. To address this limitation, we reformulate the wall free energy as a function of the average composition over the solid-fluid interface. Additionally, the previous derivation relies on an artificial treatment of describing the composition variation across the interface by a smooth monotone function, while the true nature of this variation remains unclear. By utilizing the concept of average composition, we circumvent the open question of how the composition varies across the interface region. Our work provides a thorough understanding for the construction of free energy formulations for a non-uniform system in condensed matter physics.

A new method with C-means segmentation for non-uniform image coordinate system definition in panoramic imaging employing Ladybug2 camera

A panorama ensures a stunning wide-angle field of view up to 360° representation of a scene, exceeding the limits of a normal photograph. Panoramic cameras satisfy the single-viewpoint characteristic. There are several types of panoramic cameras for 360-degree imaging. Multi-camera panoramic imaging systems pose a difficulty in obtaining a single projection center for the cameras. In a variety of practical implementations of panoramic cameras, it is possible to calculate three-dimensional coordinates from a panoramic image, especially using the Direct Linear Transformation (DLT) method. In this study, not only a defining method of the non-uniform image coordinate system is presented by utilizing the C-Means algorithm for a single panoramic image, captured with a Ladybug2 panoramic camera in a panoramic calibration room but also the use of an elliptical panoramic projection coordinate system is defined by the Singular Value Decomposition method in a panoramic view. The results of the suggested method have been compared with the DLT algorithm for a single panoramic image which defined a conventional photogrammetric image coordinate system. It has been observed that the proposed method provides more accurate results for the 3D coordinate definition.

The effect of fastener clip fatigue for high-speed railway on vehicle-track dynamic interaction: Numerical analysis and probabilistic evaluation

To investigate the vehicle-induced fatigue damage evolution of fastener clips and their impact on the vehicle-track (VT) system, a numerical dynamic model is established to achieve probabilistic evaluation. The “rain flow” counting method is adopted to describe the stress cycles of the hazard area of the clips, and the S-N curve is used to predict the fatigue life of the clips. The solution of the dynamic equation of motion is obtained by the time-domain Green's function method, which is an effective method to improve computational efficiency. A versatile iterative algorithm is adopted to solve the nonlinear system considering the damaged clips. In the probabilistic evaluation framework, a novel random field method is employed to depict the spatial variability of clips’ strength. The applicability of the model established in this work in aspects of expressing random damage of fasteners and evaluating the dynamic behavior of the system is demonstrated by different numerical examples. The results show that the dynamic responses of the train and track system significantly exacerbate as the number of train cycles increases, which is closely related to the variability and non-uniform damage of the fasteners. The probability of cumulative damage to the fasteners induced by the train follows a three-stage rule, and the fatigue damage of the non-uniform fastener system caused by the train is greater than that of the uniform situation. In addition, the short wave components of track irregularity will significantly exacerbate the damage to fasteners and therefore degrade the status of the railway line. As the driving speed increases, the damage to the fasteners also increases, but the impact of vehicle speed on the fastener damage is smaller than that of track irregularity, especially in the range of fatigue damage greater than 0.9. Therefore, maintaining the geometric smoothness of the track, controlling the uniformity of the mechanical properties of the fasteners, and reducing the driving speed are feasible measures to extend the service life of the fastener system, thereby ensuring the operation of high-speed trains.

Innovative K-Means based machine learning method for determination of non-uniform image coordinate system in panoramic imaging: a case study with Ladybug2 camera.

Currently, the practical implementations of panoramic cameras range from vehicle navigation to space studies due to their 360-degree imaging capability in particular. In this variety of uses, it is possible to calculate three-dimensional coordinates from a panoramic image, especially using the Direct Linear Transformation (DLT) method. There are several types of omnidirectional cameras which can be classified mainly as central and non-central cameras for 360-degree imaging. The central omnidirectional cameras are those which satisfy the single-viewpoint characteristic. Multi-camera systems are usually developed for applications for which two-image stereo vision is not flexible enough to capture the environment surrounding a moving platform. Although the technology based on multi-view geometry is inexpensive, accessible, and highly customizable, multi-camera panoramic imaging systems pose a difficulty in obtaining a single projection center for the cameras. In this study, not only a defining method of the non-uniform image coordinate system is suggested by means of the K-Means algorithm for a single panoramic image, captured with a Ladybug2 panoramic camera in the panoramic calibration room but also the use of an elliptical panoramic projection coordinate system definition by Singular Value Decomposition (SVD) method in panoramic view. The results of the suggested method have been compared with the DLT algorithm for a single panoramic image which defined a conventional photogrammetric image coordinate system.

Generating irregular fractals based on iterated function systems

<abstract><p>The iterated function system (IFS) is important in different fields like image compression. An important feature of such systems is that they can be used to generate fractals. Yet, for the obtained fractals, it is difficult to locally control them to generate new ones with desired structures at specific places. In this paper, we gave an attempt to solve this problem based on a nonuniform multiple function system. For this, we first analyzed the multiple function systems needed in the generation of the final desired fractals. Based on such analysis, the final fractals with desired structures at specific places can be generated using the nonuniform multiple function system. Moreover, these two procedures were summarized into two algorithms for convenience. Examples were also given to illustrate the performance of the nonuniform multiple function system and the two algorithms in this paper.</p></abstract>

Two-Phase Flow Through the PTL of PEM Water Electrolyzer: MRI Experiments and Numerical Modeling Using Phase-Field Theory

In 2021, estimation shows that the worldwide annual hydrogen production is around 94 Mt. Exploitation of native hydrogen being not mature, it is obtained by its separation from other elements by different methods such as steam methane reforming, and electrolysis of water. The latter supplied by a renewable power source will take part in the development of a green hydrogen economy [1]. In this context, Proton Exchange Membrane (PEM) Electrolyzer is a promising technology due to its flexibility and very quick adaptation to load variations. However, its current development still confronts some limitations at a large industrial scale. For instance, efficiency and durability are directly impacted by the mass transport and electrical transfer within the porous materials at the anode side. Limitation of the water supply to the catalyst layer happens once there is a poor oxygen evacuation which decreases the performance of the device by inducing high overpotential. Furthermore, the PTL has an important role as an electrical conductor for charge transfer from the catalyst layer [1]. The efficiency of all the transport phenomena through the PTL and porous electrode assembly depends on their transport properties which are related to their microstructure and operating conditions. For instance, PTL with a large pore size allows good water and gas transport, while produced electrons choose a long-distance path generating an electrical resistance higher than that in the case of PTL with a small pore size [1]. So, controlled and optimum porosity and pore size could contribute to efficient water, gas, and electron transport. To define the best porous layers morphologies, a deep and accurate understanding of the phenomena is developed in this work by combining modeling and experiments.The magnetic resonance imaging (MRI) technique was used to quantify the water content within the porous layer during the two-phase flow. Instead of the real PTL made of titanium which is paramagnetic and cannot be used in the MRI, borosilicate filters with thickness, porosity, and pore size similar to the PTL were used. After positioning the sample in the 600 MHz vertical imager (Figure 1-A), a constant water flow rate is introduced while the gas flow rate is varied. The saturation profiles measured through the porous material depend on the gas flow rate and a semi-dryness of the sample occurs (Figure 1-B) with a residual quantity trapped between pores (minimum stable water content). The water flow rate variation in the channel does not affect saturation, but a higher gas flow rate is needed to reach a minimum stable water content for higher water flow rate.The gas pressure drop through the porous medium was measured and bubble formation in the channel was also analyzed. The results show that the pressure drops and types of flow (slug, annular, and bubble flow) depend on orientation of the water channel (horizontally and vertically) and flow direction (up or downward), and on the water and gas flow rates.To reach a better understanding of the dynamic characteristics of water and oxygen transport over the PTL, the phase-field model based on the Cahn-Hilliard theory was used to simulate the two-phase flow through a porous medium [2]. In this model, the modified Navier-Stokes equations for two phases are coupled with a phase-field equation for describing the diffuse interface. Numerical simulations performed in the COMSOL® multiphysics software were carried on 2D geometries composed of spherical solid grains of different sizes, having properties similar to the PTL used in the MRI experiments. Gas is injected on one side of the sample and flows through the porous medium initially saturated and evacuated on another side in contact with the water channel (Figure 1-C). Gas flow in the porous medium and bubble formation in the water channel are studied while varying the gas and water flow rates. The simulation results give information about the gas pathways within the porous medium and the saturation profiles over time, depending on the gas/water flow rates, which will be compared with experimental results.[1] J. Parra-Restrepo, “Caractérisation des hétérogénéités de fonctionnement et de dégradation au sein d’un électrolyseur à membrane échangeuse de protons (PEM),” Université de Lorraine, 2020.[2] J. W. Cahn and J. E. Hilliard, “Free Energy of a Nonuniform System. I. Interfacial Free Energy,” The Journal of Chemical Physics, vol. 28, no. 2, pp. 258–267, Feb. 1958. Figure 1

Carlo method as the basis for in silico-modeling in the study of the pathogenesis of ischemic stroke.

The paper proposes a new mathematical model of dynamic processes in a typical spatially non-uniform biological system. The mathematical problem of modeling the dynamics of the neurovascular units of the brain under conditions of ischemic stroke is formulated and solved. An investigation of this model is conducted, and a numerical and programmatic implementation of the corresponding mathematical problem is proposed.

Combined reaction and diffusion across the interface in reactive nonuniform liquid systems

A recently introduced theoretical framework is generalized to multicomponent reactive nonuniform systems. The modified and generalized Cahn-Hilliard equation is combined with a chemical kinetics model. Kinetic rate equations, which are formulated with activities rather than concentrations, are combined with non-Fickian diffusion driven by gradients in chemical potential. Based on the incompressible density gradient theory, which provides an expression for the Gibbs energy of a nonuniform system, a generalized method is developed to model the combined reaction and diffusion associated with reactive liquid-liquid systems. A set of partial differential equations describing the temporal evolution of the mole fractions of all the involved components in the bulk phases and the spatial and temporal evolution of the mole fractions in the interface has been derived. The obtained equations were used to investigate the dynamics of the interfacial properties of a ternary mixture with a simple chemical reaction. Special attention is given to reacting mixtures with reaction rates that are much smaller than diffusion rates. In particular, it was found that the mixture will remain in phase equilibrium upon reaction and that the interfacial chemical reaction will not affect the dynamics of the overall system, the latter being only affected by the bulk phase kinetics.

PEM-based random vibration analysis under service-braking conditions on an irregular track

PurposeAccording to relevant research, non-uniform speed has a significant impact on the vehicle-track systems. Up to now, research work on it is still very limited. In this paper, the PEM is adopted to further transform it into a deterministic process to solve the vehicle’s problem of running at a non-uniform speed.Design/methodology/approachThe multi-body vehicle model has 10 degrees of freedom and the track is regarded as a finite long beam supported by lumped sleepers and ballast blocks. They are connected via linear Hertz springs. The vertical track irregularity is a Gaussian stationary process in the space domain. It is transformed into a uniformly modulated nonstationary random process in the time domain with respect to the non-uniform vehicle speed. By solving the equation of motion of the coupled vehicle-track system with the pseudo-excitation method, the pseudo-response and consequently the power spectral density and the standard deviation of the structural response can be obtained.FindingsTwo kinds of vehicle braking programs are taken in the numerical example and some beneficial conclusions are drawn.Originality/valueThe pseudo-excitation method (PEM) was used to perform the random vibration analysis of a coupled non-uniform speed vehicle-track system. Transforming the track irregularity into a uniformly modulated nonstationary random process in time domain with respect to the non-uniform vehicle speed was undertaken. The pseudo-response of the coupled system is solved by applying the Newmark algorithm with constant space integral steps. The random vibration transfer mechanism of the coupled system is fully discussed.

Parameters of State in the Global Thermodynamics of Binary Ideal Gas Mixtures in a Stationary Heat Flow.

In this paper, we formulate the first law of global thermodynamics for stationary states of the binary ideal gas mixture subjected to heat flow. We map the non-uniform system onto the uniform one and show that the internal energy U(S*,V,N1,N2,f1*,f2*) is the function of the following parameters of state: a non-equilibrium entropy S*, volume V, number of particles of the first component, N1, number of particles of the second component N2 and the renormalized degrees of freedom. The parameters f1*,f2*, N1,N2 satisfy the relation (N1/(N1+N2))f1*/f1+(N2/(N1+N2))f2*/f2=1 (f1 and f2 are the degrees of freedom for each component respectively). Thus, only 5 parameters of state describe the non-equilibrium state of the binary mixture in the heat flow. We calculate the non-equilibrium entropy S* and new thermodynamic parameters of state f1*,f2* explicitly. The latter are responsible for heat generation due to the concentration gradients. The theory reduces to equilibrium thermodynamics, when the heat flux goes to zero. As in equilibrium thermodynamics, the steady-state fundamental equation also leads to the thermodynamic Maxwell relations for measurable steady-state properties.

Fundamental Relation for the Ideal Gas in the Gravitational Field and Heat Flow.

We formulate the first law of global thermodynamics for stationary states of the ideal gas in the gravitational field subjected to heat flow. We map the non-uniform system (described by profiles of the density and temperature) onto the uniform one and show that the total internal energy U(S*,V,N,L,M*) is the function of the following parameters of state: the non-equilibrium entropy S*, volume V, number of particles, N, height of the column L along the gravitational force, and renormalized mass of a particle M*. Each parameter corresponds to a different way of energy exchange with the environment. The parameter M* changes internal energy due to the shift of the centre of mass induced by the heat flux. We give analytical expressions for the non-equilibrium entropy S* and effective mass M*. When the heat flow goes to zero, S* approaches equilibrium entropy. Additionally, when the gravitational field vanishes, our fundamental relation reduces to the fundamental relation at equilibrium.

Regular Composite Resource Partitioning and Reconfiguration in Open Systems

We consider the problem of resource provisioning for real-time cyber-physical applications in an open system environment where there does not exist a global resource scheduler that has complete knowledge of the real-time performance requirements of each individual application that shares the resources with the other applications. Regularity-based Resource Partition (RRP) model is an effective strategy to hierarchically partition and assign various resource slices among such applications. However, previous work on RRP model only discusses uniform resource environment, where resources are implicitly assumed to be synchronized and clocked at the same frequency. The challenge is that a task utilizing multiple resources may experience unexpected delays in non-uniform environments, where resources are clocked at different frequencies. This paper extends the RRP model to non-uniform multi-resource open system environments to tackle this problem. It first introduces a novel composite resource partition abstraction and then proposes algorithms to construct and reconfigure the composite resource partitions. Specifically, the Acyclic Regular Composite Resource Partition Scheduling (ARCRP-S) algorithm constructs regular composite resource partitions and the Acyclic Regular Composite Resource Partition Dynamic Reconfiguration (ARCRP-DR) algorithm reconfigures the composite resource partitions in the run time upon requests of partition configuration changes. Our experimental results show that compared with state-of-the-art methods, ARCRP-S can prevent unexpected resource supply shortfall and improve the schedulability up to 50%. On the other hand, ARCRP-DR can guarantee the resource supply during the reconfiguration with moderate computational overhead.

Large-scale phylogenetic analysis reveals genetic diversity and geographic distribution of rabies virus in South-East and South Asia.

South-East Asia (SEA) and South Asia (SA) are two important geographic regions with the most severe enzootic rabies in the world. In these regions, phylogenetic analysis of rabies virus (RABV) has been conducted only at a country level; the results obtained from different countries are scattered and unequal, with a non-uniform system to name RABV genotypes. Therefore, it is difficult to undertake origin-tracking and compare inter-country RABV evolution and transmission. To avoid the confusion in understanding and to generate a panoramic picture of RABV genetic diversity, distribution, and transmission in SEA and SA, the present study conducted a systematic phylogenetic analysis by combining all sequences representing 2368 RABV strains submitted to GenBank by 14 rabies endemic SEA and SA countries. The results showed that RABVs circulating in two regions were classified into four major clades and many subclades: the Asia clade is circulating only in SEA, the Indian subcontinent, and Arctic-like clades only in SA, while the Cosmopolitan clade has been detected in both regions. The results also showed a wide range of hosts were infected by divergent RABV subclades, with dogs being the major transmission source. However, wildlife rabies was also found to be an important issue with 6 wild carnivore species identified as potential sources of spillover risk for sylvatic rabies to humans, domestic animals, and other wild animals. Current findings indicate that the two regions have separate virus clades circulating thus indicating the absence of cross-transmission between the regions. The study emphasizes the importance of phylogenetic analysis in the regions using uniform genotyping and naming systems for rabies surveillance, to coordinate actions of member countries to eliminate dog-mediated human rabies by 2030.

Smooth mode decomposition: Theory and its applications in full-field output-only modal analysis

Full-field output-only modal analysis (OMA) became popular due to its superior spatiotemporal resolution over traditional sensing methods. It provides rich spatial dynamic information, which is essential for high-fidelity modal models, model updating, and non-intrusive health monitoring. However, the full-field sensory techniques implementation in OMA is hurdled by the excessive storage and computational requirements and the temporal aliasing effect. This paper develops a novel modal decomposition method, called smooth mode decomposition (SMD), to tackle these hurdles by exploiting the spatial dynamics and smoothness of the observed field measurements. SMD imposes the smoothness constraint on the identified mode shapes to resolve a set of orthogonal modes, called the smooth orthogonal modes (SOMs), that maximally represent the original field while also keeping the mode shape as smooth as possible. Since the SMD seeks spatially-smooth modal structures, the requirements on the temporal sampling can be relaxed. Hence, the SMD can be applied to nonuniformly and sub-Nyquist sampled full-field measurement data. Moreover, the SOMs converge to linear normal modes of uniformly distributed parameter systems, which provides a physically meaningful decomposition of the measurement data. Through a series of numerical examples, the SMD is compared to other popular covariance-based OMA methods. These examples demonstrate the merit of the proposed method when the vibration system has nonuniform system parameters and when the data is undersampled. Further, a full-field strain measurement technique, the three-dimensional digital image correlation, is utilized where spatiotemporal displacement measurements are obtained from a vibrating cantilever beam. The SMD is shown to provide accurate mode estimates with undersampled experimental data. Statistically, SMD shows its flexibility and quality in modal identification using temporally randomly captured images, which opens an avenue for alleviating storage and processing requirements for image-based full-field OMA.

Dynamic modelling of the interfacial concentration profiles of fast chemical reactions in reactive liquid–liquid systems

A theoretical framework regarding the interfacial properties of reactive liquid–liquid systems has been applied to specific model examples. Based on the kinetic rate equations, which rely on activities rather than concentrations, and the incompressible density gradient theory, which provides an expression for the Gibbs energy of a nonuniform system, the new thermodynamic treatment of inhomogeneous reactive liquid mixtures is used to study the impact of the various thermodynamic and kinetic parameters of the theoretical framework on the dynamics of chemical reactions taking place in the coexisting liquid bulk phases as well as in the interface between them. More precisely, the equations are used to describe the spatial and temporal evolution of the mole fractions in the interface and the temporal evolution of the mole fractions in the bulk phases for a ternary mixture and a simple chemical reaction. Predictions and calculations were compared to a standard model example. It was found that the studied examples follow the expected reactive and phase behaviour when varying the applied thermodynamic and kinetic parameters.

Interfacial properties of fast chemical reactions occurring in demixed ternary mixtures

A new theoretical framework regarding the interfacial properties of reactive liquid mixtures forming a liquid-liquid phase split has been introduced. Based on the kinetic rate equations, which rely on activities rather than concentrations, and the incompressible density gradient theory, which provides an expression for the Gibbs energy of a nonuniform system, a method is developed to study the dynamics of chemical reactions taking place in the coexisting liquid bulk phases as well as in the interface between them. The assumption that the chemical reaction is much faster than the diffusion leads to a set of partial differential equations describing the spatial and temporal evolution of the mole fractions of all the involved components in the interface and the temporal evolution of the mole fractions in the bulk phases. The obtained equations were used to investigate the dynamics of the interfacial concentration profiles of a ternary mixture with a large miscibility gap, applied to a simple example. Due to the fast chemical reaction and the slow diffusion, the mixture will not remain in phase equilibrium anymore. It was found that the chemical reaction reaches chemical equilibrium first in both bulk phases and afterward in the interface existing between them, which is in contrast to the classical two-film theory often used for mass transport calculations in chemical engineering.

Anti-Disturbance Boundary Control for a Wave Equation With Input Disturbance

In this article, we investigate the exponential stabilization issue of a wave equation with the external input disturbance, which is described by a nonlinear exogenous system. A novel disturbance observer is constructed to estimate the unknown input disturbance. Then, based on the proposed disturbance observer, a boundary control strategy is developed to cancel the effect of disturbance and stabilize the system. The exponential stability is proven by employing the Lyapunov’s direct method. This method can be extended to a class of flexible systems described by the hyperbolic partial differential equation met in the practical engineer area. The example of a nonuniform flexible string system is given, where the effectiveness of the proposed strategy is evaluated based on simulations.

How Flexible Is the Concept of Local Thermodynamic Equilibrium?

It has been demonstrated by using generalized phenomenological irreversible thermodynamic theory (GPITT) that by replacing the conventional composition variables {xk} by the quantum level composition variables {x˜k,j} corresponding to the nonequilibrium population of the quantum states, the resultant description remains well within the local thermodynamic equilibrium (LTE) domain. The next attempt is to replace the quantum level composition variables by their respective macroscopic manifestations as variables. For example, these manifestations are, say, the observance of fluorescence and phosphorescence, existence of physical fluxes, and ability to register various spectra (microwave, IR, UV-VIS, ESR, NMR, etc.). This exercise results in a framework that resembles with the thermodynamics with internal variables (TIV), which too is obtained as a framework within the LTE domain. This TIV-type framework is easily transformed to an extended irreversible thermodynamics (EIT) type framework, which uses physical fluxes as additional variables. The GPITT in EIT version is also obtained well within the LTE domain. Thus, GPITT becomes a complete version of classical irreversible thermodynamics (CIT). It is demonstrated that LTE is much more flexible than what CIT impresses upon. This conclusion is based on the realization that the spatial uniformity for each tiny pocket (cell) of a spatially non-uniform system remains intact while developing GPITT and obviously in its other versions.

Residual storey drift estimation of the MDOF system with the weak storey under seismic excitations using the BP network

This paper focuses on estimating residual storey drifts of multi-degree-of-freedom (MDOF) systems with the weak storey due to seismic excitations. According to the distribution of yield strength coefficients, MDOF systems are categorized into two types: a uniform MDOF system and a non-uniform MDOF system. Through elasto-plastic time history analysis, typical MDOF systems were analyzed considering the P-Δ effect under 60 earthquake records free of near-fault effects. The influences of various structural parameters on distribution characteristics of residual storey drifts along the height of the MDOF systems were investigated in detail. Finally, a back propagation (BP) network model was proposed to estimate residual storey drifts of the MDOF systems with the weak storey under seismic excitations. The results indicate that the maximum residual storey drift usually occurs at the weak storey for a non-uniform MDOF system while at the bottom for a uniform MDOF system. In addition, the larger the overall yield strength coefficient, the yield strength modification factor or the post-yield stiffness coefficient, the smaller the residual storey drift of the MDOF system on the whole. Moreover, the proposed BP model can sufficiently consider the parameters affecting residual storey drifts of the MDOF system with the weak storey, while having a good accuracy and a high efficiency in estimating the residual storey drifts.