Slope Vector Research Articles

A triangular plate element 2343 using second-order absolute-nodal-coordinate slopes: numerical computation of shape functions

In this paper, the process by which geometrical and structural matrices of plate finite elements employing absolute nodal coordinate formulation (ANCF) are constructed is studied. The kinematic and topological properties of an arbitrary plate finite element are described using universal digital code dncm that provides systematic enumeration of finite elements. This code is formed using the element’s dimension d, the number of nodes it possesses n, the number of scalar coordinates per node c, and a multiplier describing the process of transforming a conventional finite element to an ANCF element m. The detailed generation of a new type of triangular plate finite element 2343 using numerical computation of shape functions is also discussed in the paper. The new triangular element employs position vectors and slope vectors up to second-order mixed-derivative slope vector. A detailed derivation of the equations of motion of the element is also provided and examples of its numerical simulation and validation presented.

Performance Degradation Assessment of a Beam Structure by Using Wavelet Packet Energy

The evaluation on damage event of a beam structure is carried out in this study through an integration of knowledge in damage detection and signal process. A damage detection approach based on wavelet packet transform (WPT) is developed by decomposing and reconstructing the structural dynamic responses to obtain the signal energy distribution at different levels. The WPT coefficients are reconstructed to extract the signals in various frequency ranges and determine the signal energy in different frequency bands. A WPT component energy index is proposed to establish the slope vector as well as curvature vector and then the judge on the slope vector and curvature vector can indicate the damage event. Parametric study is carried out to investigate the relationship between the index amplitude and the damage extent. The results from this study demonstrate that the detection approach proposed can accurately identify the damage event in the structure.

A Bayesian Approach to Asymmetric Multidimensional Scaling

We propose a Bayesian approach to asymmetric multidimensional scaling (MDS), which incorporates an asymmetric data structure. The asymmetry is represented by the hill-climbing model, which introduces a slope vector that measures the extent of the difficulty in going from one point to another instead of vice versa, in the MDS space. By using Bayesian estimation with Markov chain Monte Carlo algorithm, both point and interval estimation of the parameters become possible, in addition to the many advantages of Bayesian estimation. The asymmetry is evaluated on the basis of the posterior credibility region of the slope vector. A numerical simulation demonstrates that the proposed method is effective for recovering the true parameter values. The proposed method is demonstrated by the analysis of brand-switching data.

Possibility of large-scale hazard monitoring by InSAR and slope vector analysis

Possibility of large-scale hazard monitoring by InSAR and slope vector analysis

M-tests for multivariate regression model

The M-estimation method is used to define the unrestricted test, restricted test and pre-test test (PTT) for testing the intercept vector of a multivariate simple regression model when it is a priori suspected that the slope vector has some specified values. The asymptotic distribution of the test statistics and the asymptotic power functions of the proposed M-tests are derived. Performances of the M-tests are compared both analytically and graphically. The analytical results as well as an illustrative simulation study to compare the size and power of the M-tests reveal a reasonable dominance of the PTT over the other two tests.

Monitoring of post-failure landslide deformation by the PS-InSAR technique at Lubietova in Central Slovakia

Interferometric synthetic aperture radar data from ERS and ENVISAT sensors were utilized in the analysis of the post-failure deformations in the area of Lubietova town in Central Slovakia. The catastrophic landslide of 1977 together with surrounding landslides in the Lubietova area were analysed with the help of persistent scatterers (PS) technique in order to evaluate recent and past deformations of the unstable slopes. Although long-term precise geodetic monitoring of the 1977 landslide revealed differential deformations inside the sliding mass, due to the lack of the PS located inside the landside caused by temporal decorrelation, unfortunately, these records could not be directly compared. The adjacent landslides with sufficient number of PS were analysed by transformation of the line of sight displacements recorded by the sensors to the slope vector direction. This procedure allowed identification of the precise boundaries of the actively moving landslide parts and the updating of the landslide inventory for the Lubietova area.

Evaluation of terrain geomorphometric characteristics for ground clearance charts production

Evaluation of terrain geomorphometric characteristics for ground clearance charts production

운동부하 심전도를 이용한 중년 남성들의 걷기 운동이 ST/HR 경사 및 QRS 벡터에 미치는 영향

본 연구는 중년 남성들을 대상으로 3년간 1년에 1회씩 3차례에 걸쳐 운동부하 검사 시 심전도 반응을 측정하여 야외 및 트레드밀 걷기 운동 참여 여부에 따라 부하 심전도의 변화에 어떠한 양상이 나타나는지를 규명하고자, 안정 시 신체조성 분석, 운동부하 검사 시 심전도 반응을 측정하였다. 안정 시 신체조성 분석은 체지방율과 BMI를 측정하였고, 안정 시 및 운동부하 검사 시 심전도 반응은 ST/HR 경사 및 QRS 벡터를 측정하였는데, 그 결과는 다음과 같다. 1. ST/HR 경사의 변화에 있어서 운동 6분부터 통제 집단은 감소하기 시작하여 운동 9분과 peak시에 <TEX>$2.4\;{\mu}V/bpm$</TEX> 이하로 감소하여 허혈 증상이 나타났다. 2. QRS 벡터의 축 각도에 있어서 안정 시 전면 축은 시간이 경과함에 따라 통제 집단이 우측으로 유의하게 편향되었고, 안정 시 수평면 축은 시간이 경과함에 따라 통제 집단이 등 쪽으로 유의하게 향하였다. 안정 시 수평면 파고의 길이에 있어서 통제 집단은 시간이 경과함에 따라 유의하게 감소하였고 걷기 운동 집단은 유의하게 증가하였다. 결론적으로 비 활동의 중년 남성들은 운동 중 심근 허혈 유발, QRS 벡터의 편향 등이 현저하게 나타난 반면, 규칙적인 야외 및 트레드밀 걷기 활동에 참여한 중년 남성들은 심혈관계 질환 위험 요소의 감소로 심장기능이 향상된 결과를 알 수 있었다. The purpose of this study was to investigate the changes of long term ECG response in a company with middle-aged male employees. Subjects were 60 men who were 40~55 years old. We enrolled 30 exercise group subjects into a 3-year exercise program. In measurement index, body composition was measured by % body fat and BMI. Exercise stress test analyses were measured using ST/HR slope and QRS vector. Statistical analysis was performed using analysis of repeated ANOVA. Results of this study were as follows: In ST/HR slope, the control group showed symptoms of ischemia after nine minutes of exercise. In the rest frontal axis of the QRS vector, the control group had a tendency towards right axis deviation. In the rest horizontal amplitude of the QRS vector, the control group had a tendency to show a significant decrease, but it was increased significantly in the exercise group. These findings suggest that inactive company workers was showed a decrease of exercise capacity, early diagnosis exercise-induced ST depression, and prolonged deviation of QRS vector, but that cardiac function could be elevated in active middle aged men through regular exercise program participation.

Human Regions Extraction with Slight Movements Using Chronological Difference of Density Slope Vector

Human Regions Extraction with Slight Movements Using Chronological Difference of Density Slope Vector

Biased estimation in a simple multivariate regression model

Estimation of the intercept vector in a simple multivariate normal regression model is considered, when it is a priori suspected that the slope vector may be restricted to a subspace. We propose two new Stein-type and preliminary test estimators for the parameter vector. The positive-part estimator is superior to the usual Stein-type estimator, and the proposed preliminary test estimator outperforms the standard preliminary test estimator regardless of the correctness of the nonsample information. The relative dominance picture of estimators is presented.

High Resolution Digital Elevation Models - A New Data Source

High resolution digital elevation models (DEMs) can now be produced for large areas of Australia. This paper will describe the method of producing DEMs and some of the applications. The change in technology which has made possible routine generation of height data for large areas, is soft photo-grammetry. In the past, the method of determining height was by matching points on two airphoto stereopairs. This was accomplished manually which made for a tedious and time consuming process. The advent of computer software that can match features on stereopairs has meant that DEMs can be created much more quickly. The procedure is to scan the diapositives of the air photographs with a geometrically accurate scanner at high resolution (15?30 microns). This will give a pixel size of 1.5 metres for a 1:50,000 scale photo. Internal and external distortion is then removed from the scanned images by internal, relative and absolute orientation procedures. The images are then resampled as epipolar pairs. The final procedure is to automatically match common features on both of the stereopairs. Changes in the X parallax give the height or Z value. The DEMs are accurate to within ±1 pixel i.e. 1.5 metres for standard 1:50,000 scale photography or 25 cm for 1:10,000 photography. This high resolution allows for a number of novel applications, including: - identify topographic anomalies associated with mineralisation (e.g. kimberlite lows, silicified highs); - georectify photographs to produce orthophotos - 3D visualisation, 3D PhotomapsO, and terrain draping; - structural analysis using shaded relief images; - landform analysis including palaeo surface reconstruction; - slope vector maps for soil sampling and geochemical dispersion; - drainage maps and drainage divides for stream sampling programs; - height corrections for high resolution gravity surveys. Images for these applications will be shown for the Laverton 1:50,000 sheet area in Western Australia.

Improved estimation in a multivariate regression model

The problem of estimating the intercept vector in a simple multivariate regression model is considered when it is a priori suspected that the slope vector may be restricted to a subspace. We propose estimators based on the outcome of the pre-test and then a shrinkage technique is employed. This estimator may be viewed as an improvement over the usual preliminary test estimator (PTE). It is important to note that the proposed estimator dominates the classical estimator over a large portion of the parameter space which is wider than that of the PTE. Furthermore, the proposed estimator is also superior in relative bias and efficiency to the usual PTE. Moreover, an optimal rule for the choice of the level of significance (α) for the preliminary test is presented. Table for the optimum selection of α is also provided for the use of the proposed estimator.

Sensitivity analysis for Box-Cox power transformation model: Contrast parameters

SUMMARY Sensitivity analysis is an important tool for the evaluation of scientific models. We consider the Box-Cox power transformation model and study the sensitivity for the estimated slope vector when the transformation parameter is perturbed. This is a key issue in the debate among Bickel & Doksum (1981), Box & Cox (1982) and Hinkley & Runger (1984) on the application of the power transformation model. Hinkley & Runger (1984) conjectured that Box & Cox's (1964) z transformation would eliminate asymptotically the sensitivity for the estimated slope vector. We establish this conjecture under appropriate symmetry conditions on the joint distribution for the regressors, x. When the true transformation is logarithmic, the conjecture holds if the distribution for x is axially symmetric. For other power transformations, the conjecture holds if x is multivariate normal. We also consider a weaker version of Hinkley & Runger's conjecture, namely, the z transformation would achieve the best possible reduction in the sensitivity. We establish this weaker conjecture under less restrictive symmetry conditions which only involve the marginal distribution for xfl. Both conjectures might fail when those symmetry conditions are not satisfied. Two examples are given to illustrate the limitations of the conjectures. Sensitivity analysis is an important tool for the evaluation of scientific models. Many scientific models include some nuisance parameters which are not known precisely. It is usually desirable for the model output to be stable with respect to those parameters. The performance of the model can be questionable if the model output is highly sensitive to those parameters. It is therefore useful to carry out a sensitivity analysis, in which those parameters are perturbed, the model output is derived under the perturbed parameters and compared with the model output prior to the perturbation. We will study the sensitivity analysis for the Box-Cox power transformation model with respect to the specific transformation taken. Let {(yi, xi), i = 1, . . . , n} be the observed data, where yi denotes a positive scalar outcome, and xi denotes a p-dimensional row vector of regressors. Let the transformed outcome be

Regression Analysis Under Link Violation

We study the behavior of regression analysis when there might be some violation of the assumed link function, the functional form of the model which relates the outcome variable $y$ to the regressor variable $\mathbf{x}$ and the random error. We allow the true link function to be completely arbitrary, except that $y$ depends on $\mathbf{x}$ only through a linear combination $\beta\mathbf{x}$. The slope vector $\beta$ is identified only up to a multiplicative scalar. Under appropriate conditions, any maximum likelihood-type regression estimate is shown to be consistent for $\beta$ up to a multiplicative scalar, even though the estimate might be based on a misspecified link function. The crucial conditions are (1) the estimate is based on minimizing a criterion function $L(\theta, y)$ which is convex in $\theta$, where $\theta = a + b\mathbf{x}$, (2) the expected criterion function $E\lbrack L(a + b\mathbf{x}, y)\rbrack$ has a proper minimizer and (3) the regressor variable $\mathbf{x}$ is sampled randomly from a probability distribution such that $E(b\mathbf{x}\mid\beta\mathbf{x})$ is linear in $\beta\mathbf{x}$ for all linear combinations $b\mathbf{x}$. The least squares estimate, the GLM estimates and the $M$-estimates for robust regression are discussed in detail. These estimates are asymptotically normal. With the assumption that the regressor variable has an elliptically symmetric distribution, we show that under a scale-invariant null hypothesis of the form $H_0: \beta W = 0$, the asymptotic covariance matrix for $\hat{\beta}W$ is proportional to the one derived by treating the assumed link function as being true. The Wald test as well as the likelihood ratio test for a scale-invariant null hypothesis has the correct asymptotic null distribution after an appropriate rescaling of the test statistic to account for the proportionality constant between the two asymptotic covariance matrices. For normally distributed $\mathbf{x}$, the rescaling factor for $M$-estimates is the same as the one used in robust regression, while the rescaling factor for GLM estimates is related to adjustment for overdispersion. Confidence sets can be constructed by inverting Wald's tests. The impact of the violation of linear conditional expectation condition 3 is discussed. A new dimension is added to the regression diagnostics by exploring the elliptical symmetry of the design distribution. A connection between this work and adaptive estimation is briefly discussed.

Distribution-free and link-free estimation for the sample selection model

Abstract The prevalent estimation methods for the sample selection model rely heavily on parametric assumptions and are sensitive to departures from the underlying parametric assumptions [see, e.g., Goldberger (1983)]. We propose an alternative estimation method, the corrected maximum likelihood estimate, which is consistent for the slope vector in the outcome equation up to a multiplicative scalar, even through the parametric model on which the estimate is based might be misspecified. As an important corollary, it follows from our result that Olsen's (1980) corrected ordinary least squares estimate is consistent if the outcome equation is linear, without requiring Olsen's assumptions on the joint error distribution.

Testing for linearity

A nonparametric large sample test is proposed for testing the linearity of a regression model with independent and identically distributed errors satisfying only a very mild tail condition. The statistic is based on the functional least squares estimator of the slope vector. The test is applied to the stack loss data.