Proceedings; XXI International Congress for Photogrammetry and Remote Sensing: Proceedings; XXI International Congress for Photogrammetry and Remote Sensing

Chen, Jun

Bibliographic data

Multivolume work

Persistent identifier:: 1877007366

Author:: Albert, Franz W.

Title:: Die Technische Mechanik im Hochbau

Sub title:: ein Leitfaden zum Gebrauche für den Unterricht an Baugewerkenschulen und beim Entwerfen und Dimensioniren in der Praxis : mit 19 lithographirten Tafeln in besonderem Atlas

Year of publication:: 1881

Place of publication:: Plauen; Hannover

Publisher of the original:: Verlag von A. Hohmann

Identifier (digital):: 1877007366

Language:: German

Additional Notes:: Text- und Tafelband sind 1881 erschienen

Publisher of the digital copy:: Technische Informationsbibliothek (TIB)

Document type:: Multivolume work

Volume

Persistent identifier:: 1877007412

Author:: Albert, Franz W.

Title:: Die Technische Mechanik im Hochbau

Scope:: VIII, 146 Seiten, 2 ungezählte Blätter

DOI:: 10.14463/KXP:1877007412

Year of publication:: 1881

Place of publication:: Plauen

Publisher of the original:: Verlag von A. Hohmann

Identifier (digital):: 1877007412

Illustration:: Illustrationen

Signature of the source:: a 3325

Language:: German

Usage licence:: Public Domain Mark 1.0

Publisher of the digital copy:: Technische Informationsbibliothek Hannover

Place of publication of the digital copy:: Hannover

Year of publication of the original:: 2023

Document type:: Volume

Collection:: Civil engineering; Mechanical engineering; Physics; Materials sciences

Preface

Title:: Vorwort.

Document type:: Multivolume work

Structure type:: Preface

The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B2. Beijing 2008 198 Means and variances of whole 137 International Meteorological Stations from 1951-2002 are calculated and then the sequence mean temperature plot for the whole study area was drawn (see Figure 3). As is clearly depicted in Figure 3, sample means from 1951-1990 are upward trend and indicate that series are non-stationary. Structure analysis of sample data discovers explicitly spatial trend for use of kriging model (see Figure 4). This conclusion leads to use ANN for space-time trend modeling. 3.3 The ANN model to predict the space-time (or trend) patterns The ANN model was built to capture non-linear space-time trends (see Section 2.1). The implemented neural network can be seen in Figure 5. The ANN model used had the following parameters: three input neurons with linear activation function of spatial coordinates longitude (x), latitude (y), and time t (year), which were normalized to a specified range [0, 1]; one hidden layer with five processors and a sigmoid activation function; an output neuron with sigmoid activation function, describing annual average temperature at spatial location (x,>») and time t. This choice was based on the analysis of the training and testing errors. 3.4 The STARMA to model the space-time variances 3.4.1 Define the spatial weight matrix First, ANN residuals are analyzed. The isotropic semi- variogram model, y(/?) , with a gaussian function was used to analyze space-time variance structures of ANN residuals. Table 1 shows the parameters of sample ANN residual spatial variance structures at different years. Year Range (km) Partial Sill (C) Nugget (C n ) Sill (C 0 +C) Co/sill (%) 1951 1484.8 9.019 7.826 16.845 46.459 1955 1493.8 6.262 4.090 10.352 39.509 1960 1532.4 5.264 2.540 7.804 32.547 1965 1463.2 6.671 1.312 7.983 36.435 1970 1541.9 16.939 9.833 26.772 36.729 1975 1552.3 4.245 2.510 6.755 37.158 1980 1421.0 4.537 2.567 7.104 36.135 1985 1502.9 4.780 2.841 7.621 37.279 1990 1402.1 3.916 2.501 6.417 38.975 Table 1 Summary of sample ANN residuals isotropic semi- variogram analysis parameters in past several decades Figure 5. Structure of the implemented ANN model. It should be noted with attention that training data were organized as a sample, the length of which is 137x42, and there are 137 outputs at each year t, which represent annual average temperature forecast at 137 stations Then, weights were defined according to the Euclidean distance between two points as jw(h) = [(C 0 + Ci)-y(/z)]/(C 0 + Cj) h<a (4) [w(/j) = 0 h = 0 or h > a where w(h) is a weight function about distance h , y(h) is the gaussian semi-variogram function value, a is the spatial correlation distance (or range), C is partial sill value, Co is nugget value, C + Cq is the sill or sample variance. In the ANN model, the training data were organized as a sample in which length is 137X(42) and there are 137 outputs in each year t , which represent fitted annual average temperature at 137 stations. The fitted results in 1970, 1980, and 1990 for large-scale deterministic space-time trends are presented in Figure 6, which shows that the ANN model captured non-linear space-time trends. l97**NN?i8M 1MO ANN FAtHt 'MWAMNFXtM Figure 6. Non-linear space-time trends captured by the ANN model Thus, w(h) tends to decrease as h increases. That is, if values are similar (distance smaller), weight will be close to 1, and if values are dissimilar (distance larger), weight will be close to 0. These weights are expressed as a hierarchical ordering of spatial neighbours. The definition of spatial order represents an ordering in terms of Euclidean distance of all stations surrounding the locations of interest. First order neighbours are those “closest” to the station point of interest. Second order neighbours should be “farther” away than first order neighbours, but “closer” than third order neighbours (Pfeifer and Deutsch 1980). In the study, spatial order is defined as one according to range of spatial autocorrelation. 3.4.2 STARMA Model To identify spatial lag and temporal lag order of STARMA model, the sample space-time autocorrelation and partial autocorrelation function of ANN residuals is presented in Table 2 and Table 3. The sample residuals’ space-time autocorrelations appear to tail off with both space and time; the sample residuals’ space-time partial autocorrelations seem to cut off at temporal lag second, at spatial lag the zero and the first so that this can be identified as a STARMA (3,0), where STARMA stands for space-time autoregressive moving average

Access restriction

Copyright

fullscreen: Proceedings; XXI International Congress for Photogrammetry and Remote Sensing (Part B2-1)

Multivolume work

Volume

Preface

Table of contents

Cite and reuse

Volume

Chapter

Image

Image fragment

Citation links

Citation recommendation