Magnitude bounds of generalized frequency response functions for nonlinear Volterra systems described by NARX model

In order to reveal the relationship between system time domain model parameters and system frequency response functions, new magnitude bounds of frequency response functions for nonlinear Volterra systems described by NARX model are established. The magnitude bound of the nth-order generalized frequency response function (GFRF) can be expressed as a simple n-degree polynomial function of the magnitude of the first order GFRF, whose coefficients are functions of the model parameters and frequency variables. Thus the system output spectrum can also be bounded by a polynomial function of the magnitude of the first order GFRF. These results demonstrate explicitly the analytical relationship between model parameters and system frequency response functions, and provide a significant insight into the magnitude based analysis and synthesis of nonlinear systems in the frequency domain.     

相关乘性和加性高斯白噪声激励下周期势系统的随机共振

研究了外加周期信号作用下,相关高斯乘性和加性白噪声激励下周期势系统的随机共振.利用线性响应理论,计算了系统输出信号的功率谱密度、振幅、相位差.研究结果表明:当加性噪声强度和关联系数不变的情况下,通过调整乘性噪声强度可以出现随机共振;关联系数的正负以及大小对随机共振的影响较小.当乘性噪声强度较小时,输出信号的振幅和相位差曲线有一个单峰出现,即出现随机共振现象,能量从噪声向信号进行转化.随着噪声强度的增大,随机共振现象消失,噪声由增大系统的有序程度渐渐变为增大系统的无序程度.     

光谱响应差异对高精度交叉定标的影响——以FY-3A/MERSI与EOS/MODIS为研究实例

分析了MERSI与MODIS间光谱响应差异对测量表观反射比的影响。正演模拟结果显示,在极区冰雪情况下,MERSI与MODIS测量得到的表观反射比之间的相对差异是关于MODIS所测表观发射比的二次函数。MERSI的前4个通道与对应的MODIS通道之间的相对差异在0~0.8%,0~2%,0.5%~2.5%,-1.8%~-0.8%之间。将正演模拟得到的对光谱响应差异的修正关系应用到具体的SNO测量后,MERSI前3个通道的表观反射比与修正后MODIS的表观反射比之间的相对差异减小到了3%以内。MERSI的1、2通道在红外波段也有响应,这部分响应在极区冰雪条件下对表观反射率的影响在0.5%左右,基本可以忽略。     

Lyapunov characterization of forced oscillations

This paper develops a Lyapunov approach to the analysis of input-output characteristics for systems under the excitation of a class of oscillatory inputs. Apart from sinusoidal signals, the class of oscillatory inputs include multi-tone signals and periodic signals which can be described as the output of an autonomous system. The Lyapunov approach is developed for linear systems, homogeneous systems (differential inclusions) and nonlinear systems (differential inclusions), respectively. In particular, it is established that the steady-state gain can be arbitrarily closely characterized with Lyapunov functions if the output response converges exponentially to the steady-state. Other output measures that will be characterized include the peak of the transient response and the convergence rate. Tools based on linear matrix inequalities (LMIs) are developed for the numerical analysis of linear differential inclusions (LDIs). This paper's results can be readily applied to the evaluation of frequency responses of general nonlinear and uncertain systems by restricting the inputs to sinusoidal signals. Guided by the numerical result for a second order LDI, an interesting phenomenon is observed that the peak of the frequency response can be strictly larger than the L₂ gain.     

1/2分数阶线性随机动力系统的非平稳响应解析解

提出随机激励作用下1/2分数阶线性系统非平稳响应解析解的一种新方法.首先,利用特征向量展开得到1/2分数阶阻尼系统的脉冲响应函数解析表达;之后,基于Laplace变换计算得到响应功率谱密度的解析表达式和系统均方响应.通过白噪声、调制白噪声和调制修正金井清谱三种不同随机激励类型的数值算例,利用与蒙特卡洛模拟所得结果对比证明该方法的准确性和适用性.     

On the estimation of transfer functions

This paper treats the close conceptual relationships between basic approaches to the estimation of transfer functions of linear systems. The classical methods of frequency and spectral analysis are shown to be related to the well-known time domain methods of prediction error type via a common “empirical transfer function estimate”. Asymptotic properties of the estimates obtained by the respective methods are also described and discussed. An important feature that is displayed by this treatment is a frequency domain weighting function that determines the distribution of bias in case the true system cannot be exactly described within the chosen model set. The choice of this weighting function is made in terms of noise models for time-domain methods. The noise model thus has a dual character from the system approximation point of view.     

转子突加不平衡的碰摩响应

航空发动机等高速旋转机械在工作时会出现叶片掉块、飞失等突加不平衡情况,突加不平衡引发的碰摩可能导致转子失稳和系统的破坏.本文对一个具有非线性支承刚度的跨中转子在突加不平衡时的碰摩响应进行了数值仿真,计算发现系统在突加不平衡发生后将会出现6种不同的碰摩响应形式,给出了参数-突加不平衡转速平面上不同稳态动力学响应模式的边界曲线,同时针对系统在突加不平衡发生后减速通过临界转速时的失稳现象,给出了失稳边界,研究表明增大转子阻尼,降低转静接触刚度和摩擦系数,可以减小失稳的转速范围.分析了参数对系统瞬态响应的影响,瞬态响应随转速的变化会发生跳跃,而瞬态响应随突加不平衡偏心量的变化,在低于共振转速时是平缓增大的,而在高于共振转速时也会有跳跃发生.     

An Adaptive and Cost-Based Intrusion Response System

An Adaptive and Cost-Based Intrusion Response System (ACBIRS) is presented in this paper. The designed system analyzes alerts from the Intrusion Detection System (IDS) and evaluates the attack cost, based on the probable damage of attacks on the protected system. Later on, a response is deployed to thwart the attack and prevent the attacker from reaching his/her goals. The proposed response selection approach is a cost-based method that considers attack features, including type of the attack, severity of the attack, value of targeted host/hosts services, and their data to prioritize alerts. Alerts will be responded with respect to their priorities. The selected responses are based on a measure called Response Merit (RM). The balance between attack damage cost, response cost together with the effectiveness of the response to countermeasure previous attacks determine the RM. In contrast to other Intrusion Response Systems (IRS), ACBIRS not only consists of the attack and response measures but also includes response feedback supervision that is proposed in this paper for the first time. ACBIRS allows responses to be adaptive in changing environments through success and failure assessment of previously deployed responses. Experiments show that ACBIRS can successfully prevent 92% of intrusions with only 3% disruption on benign traffic.     

Efficient computation of higher order frequency response functions for nonlinear systems with,and without,a constant term

The behaviour of a nonlinear system can be profoundly affected by the presence of a constant or dc term in the system governing equation. These changes are reflected in the nonlinear frequency response characteristics of the system which provide a powerful insight into the system's dynamics. In this article, a new and efficient algorithm is presented for computing the higher order Volterra frequency response functions from nonlinear time-domain models that may contain a constant term. A comparison with previous methods is included to demonstrate the significant gains in computational efficiency that are achieved using the new method. The algorithm is applicable to systems modelled by nonlinear differential, or difference, equations and is easily automated. Several examples are used to illustrate the method, and to highlight the importance of dc terms in nonlinear system analysis.     

Optimization of dynamic response using a monolithic-time formulation

The design of systems for dynamic response may involve constraints that need to be satisfied over an entire time interval or objective functions evaluated over the interval. Efficiently performing the constrained optimization is challenging, since the typical response is implicitly linked to the design variables through a numerical integration of the governing differential equations. Evaluating constraints is costly, as is the determination of sensitivities to variations in the design variables. In this paper, we investigate the application of a temporal spectral element method to the optimization of transient and time-periodic responses of fundamental engineering systems. Through the spectral discretization, the response is computed globally, thereby enabling a more explicit connection between the response and design variables and facilitating the efficient computation of response sensitivities. Furthermore, the response is captured in a higher order manner to increase analysis accuracy. Two applications of the coupling of dynamic response optimization with the temporal spectral element method are demonstrated. The first application, a one-degree-of-freedom, linear, impact absorber, is selected from the auto industry, and tests the ability of the method to treat transient constraints over a large-time interval. The second application, a related mass-spring-damper system, shows how the method can be used to obtain work and amplitude optimal time-periodic control force subject to constraints over a periodic time interval. This research was performed while the first author held a National Research Council Research Associateship Award at the Air Force Research Laboratory. An early version of this paper was presented at the 46th AIAA Aerospace Sciences Meeting and Exhibit, Jan 7–10, 2008, Reno, Nevada.     

Nonlinear continuous multi-response problems: a novel two-phase hybrid genetic based metaheuristic

Generally the most real world production systems are tackling several different responses and the problem is optimizing these responses concurrently. This study strives to present a new two-phase hybrid genetic based metaheuristic for optimizing nonlinear continuous multi-response problems. Premature convergence and getting stuck in local optima, which makes the algorithm time consuming, are common problems dealing with genetic algorithms (GAs). So we hybridize GA with a clustering approach and particle swarm optimization algorithm (PSO) to make a balanced relationship between time consuming and premature termination. The proposed algorithm also tries to find Ideal Points (IPs) for response functions. IPs are considered as improvement measures that determine when PSO should start. PSO based local search exploit Pareto archive solutions to enhance performance of the algorithm by expanding the search space. Since there is no standard benchmark in this field, we use two case studies from distinguished paper in multi-response optimization and compare the results with some of the mentioned algorithms in the literature. Results show the outperformance of the proposed algorithm than all of them.     

CBA-neural network control of a non-linear full vehicle model

In this paper, the dynamic behavior of a non-linear eight degrees of freedom vehicle model having active suspensions and passenger seat controlled by a neural network (NN) controller is examined. A robust NN structure is established by using principle design data from the Matlab diagrams of system functions. In the NN structure, Classic Back-Propagation Algorithm (CBA) is employed. The user inputs a set of x₁ − x₁₆ while the output from the NN consists of f₁ − f₁₆ non-linear functions. Further, the Permanent Magnet Synchronous Motor (PMSM) controller is also determined using the same NN structure. According to various tests of the NN structure it is demonstrated that the model is able to give highly sensitive outputs for vibration condition, even using a more restricted input data set. The non-linearity occurs due to dry friction on the dampers. The vehicle body and the passenger seat using PMSM are fully controlled at the same time. The time responses of the non-linear vehicle model due to road disturbance and the frequency responses are obtained. Finally, uncontrolled and controlled cases are compared. It is seen that seat vibrations of a non-linear full vehicle model are controlled by NN based system exactly.     

Gravitational wave signal templates,pattern recognition,and reciprocal Eulerian gamma functions

The direct   detection of Gravitational Waves (GWs) is one of the most challenging problems in experimental gravitation today. It necessitates the use of highly advanced large laser interferometers such as LIGO, VIRGO, LISA, TAMA 300, GEO 600 and AIGO. The analysis of the data from such instruments requires and combines the expertise from a multitude of scientific disciplines. The verification of a detected signal demands an effective way to distinguish the source signal from the background noise. Such a study is required for an all-sky search to determine the ?$?$ and θ$\theta$ angles on the sky of gravitational wave sources and their frequencies. In this paper, we present analytical solutions and associated numerical approximations for the inner products employed in matched filtering a GW signal using templates. An exact closed-form expression for the inner products is rigourously derived using the special functions of mathematical physics. The inner products involve reciprocal Eulerian gamma functions, which occur in the study of many diverse phenomena. The spectral noise density of the VIRGO GW detector is shown to be amenable to our analysis. Spectral noise densities like those for LIGO and GEO 600, although different and in a slightly more restricted frequency band, are likewise amenable. We study numerical computation of the inner products, estimate the computational time of the solution on serial and parallel computers, and show the efficiency of the resulting algorithms. The fitting factor that indicates the goodness of fit between a signal and a template is given in closed-form and computed numerically. The numerical plots display an approximate symmetry in the template ?$?$ and θ$\theta$ domain.     

Modeling dichotomous item responses with free-knot splines

Item response theory (IRT) models are a class of generalized mixed effect (GME) models used by psychometricians to describe the response behavior of individuals to a set of categorically scored items. The typical assumptions of IRT are Unidimensionality(U) of the random effect; Conditional (or Local) Independence (CI), the item responses are independent given the random effect; and Monotonicity (M), the probability of a correct response is a non-decreasing function of the random effect. The simple parametric models available in the psychometric literature have proved to be too restrictive in many data sets. Non-parametric regression models are a powerful tool for the estimation of non-linear curves, and have been used in IRT as a flexible way to model the item response function. This paper develops a new method for the non-parametric estimation of item response functions based on reversible-jump Markov Chain Monte Carlo, and demonstrates the practicality of the method by examining two data sets.     

Photo-realistic visualization of seismic dynamic responses of urban building clusters based on oblique aerial photography

Highly realistic visualizations of seismic dynamic responses of building clusters are critical for earthquake safety education. To this end, a photo-realistic visualization method of the seismic dynamic responses of urban building clusters is proposed based on oblique aerial photography. Specifically, a sparsification algorithm of aerial photograph footprints and the model optimization solutions are designed to reduce the size of a city model reconstructed by oblique aerial photography. A building segmentation algorithm based on Boolean operations and building footprints is designed to separate buildings from a reconstructed three-dimensional city model. A visualization algorithm for the seismic dynamic responses of building clusters is designed based on the Callback mechanism, by which the shaking process of building clusters can be realistically displayed according to the results of a city-scale nonlinear time-history analysis. New Beichuan City in China is adopted as a case study to visualize seismic dynamic response. The visualization produced by the proposed method is more realistic than that of the finite element method and can support decision making on earthquake safety actions. The outcome of this study provides well-founded and photo-realistic scenes of the seismic dynamic response of building clusters and has promising application prospects for earthquake safety education.     

An efficient estimation of probability of first-passage in a linear system

Reliability analysis of a structure under random vibratory loads involves estimation of the probability of the response exceeding a limit. The classical, brute force approach to such analysis is the Monte Carlo method. However, due to its slow convergence rate, it is often impractical for large-scale engineering structures. In many engineering applications, such as offshore platforms under wave loads, the excitation is represented by Power Spectral Density (PSD) functions. Random time histories of the excitation are generated using a linear combination of sinusoids that are consistent with the PSD of input load. This paper proposes a method that reduces the computational cost of MCs of a linear system with a separable performance function; that is, a function that can be decomposed into parts and calculated independently. The method generates sinusoidal functions of the excitation, finds the system response to each sinusoid, and stores the responses in a database. Then it samples with replacement the sinusoids of the response from the database, finds the system response to the superposition of these sinusoids and checks for failure. This procedure yields a very large number of values of the failure indicator function even from a database with a modest number of sinusoids because it uses sampling with replacement. The efficiency of the proposed approach is demonstrated by estimating the probability of the first excursion in a ten-bar truss model. In this example, the method predicts the probability of failure using less than 0.2 % of the calculated values of the failure indicator function than the standard MCs.     

Criteria for Response Monotonicity Preserving in Approximation of Fractional Order Systems

In approximation of fractional order systems, a significant objective is to preserve the important properties of the original system. The monotonicity of time/frequency responses is one of these properties whose preservation is of great importance in approximation process. Considering this importance, the issues of monotonicity preservation of the step response and monotonicity preservation of the magnitude-frequency response are independently investigated in this paper. In these investigations, some conditions on approximating filters of fractional operators are found to guarantee the preservation of step/magnitude-frequency response monotonicity in approximation process. These conditions are also simplified in some special cases. In addition, numerical simulation results are presented to show the usefulness of the obtained conditions.      

基于虚拟仿真技术的车架动态响应特性分析

采用ALGOR有限元分析软件对车架进行模态分析,得出了前10阶振型及固有频率。运用二自由度汽车振动模型,建立了系统的运动微分方程并利用Matlab中的Simulink模块对车架的振动情况做出了仿真。利用路面谱仿真得到的路面激励信号作为输入,对车架进行动力响应模拟,得到了车架在典型路面上的动态响应特性,为车架的结构优化提供了理论依据。     

波谱响应函数和波宽对地表温度反演的影响

分析了波谱响应函数和波宽对红外数据反演地表温度的影响。结果表明,波谱响应函数对温度反演的影响与传感器波段设置相关,误差随波宽变大而增加。Landsat、CBERS和环境卫星等宽波段红外数据的通道辐亮度和温度的关系,用有效波长比中心波长代替积分效果更好,但都存在一定误差,针对这些传感器数据的单通道算法须考虑波谱响应的差别。窄波段的MDIS地表温度反演,有效波长比中心波长代替积分效果更好,能满足精度要求。Terra和Aqua的MODIS波谱响应函数差别很小,可相互结合提高地表温度的反演精度。     

Convergence analysis of BP neural networks via sparse response regularization

Backpropagation (BP) algorithm is the typical strategy to train the feedforward neural networks (FNNs). Gradient descent approach is the popular numerical optimal method which is employed to implement the BP algorithm. However, this technique frequently leads to poor generalization and slow convergence. Inspired by the sparse response character of human neuron system, several sparse-response BP algorithms were developed which effectively improve the generalization performance. The essential idea is to impose the responses of hidden layer as a specific L₁ penalty term on the standard error function of FNNs. In this paper, we mainly focus on the two remaining challenging tasks: one is to solve the non-differential problem of the L₁ penalty term by introducing smooth approximation functions. The other aspect is to provide a rigorous convergence analysis for this novel sparse response BP algorithm. In addition, an illustrative numerical simulation has been done to support the theoretical statement.