Environmental Data Analysis: Methods and Applications

✍ Scribed by Zhihua Zhang

• Publisher: De Gruyter
• Year: 2023
• Tongue: English
• Leaves: 400
• Edition: 2
• Category: Library

✦ Synopsis

There are some books that target the theory of the finite element, while others focus on the programming side of things. Introduction to Finite Element Analysis Using MATLAB and Abaqus accomplishes both. This book teaches the first principles of the finite element method. It presents the theory of the finite element method while maintaining a balance between its mathematical formulation, programming implementation, and application using commercial software. The computer implementation is carried out using MATLAB, while the practical applications are carried out in both MATLAB and Abaqus. MATLAB is a high-level language specially designed for dealing with matrices, making it particularly suited for programming the finite element method, while Abaqus is a suite of commercial finite element software.

• Includes more than 100 tables, photographs, and figures
• Provides MATLAB codes to generate contour plots for sample results

To deeply mine features and quickly capture useful information inside environmental big data, in the second edition of our book “Environmental Data Analysis: Methods and Applications”, we add emerging network models: neural networks, complex networks, downscaling analysis and streaming data on networks. Neural networks can imitate nonlinear non-stationary hidden links inside the environmental system through a learning process and then make exact predictions, but they do not need to directly extract these hidden links. Complex networks can fill gaps in understanding complex nonlinear dynamical processes governing the environmental system. Changes in environmental evolution over time can be detected by local, global, topological, and spectral structures of associated networks. Downscaling analysis can overcome the sparsity of environmental monitoring sites and produce a high-resolution environmental evolution map. Streaming data on networks can reveal the complexity of dynamic environmental evolutions and make near-real-time management and decisions. All these models and algorithms have been rapidly developed since the release of the first edition of our book.

Networks are becoming an emerging brand-new tool to fill gaps in understanding the complex nonlinear dynamical processes governing environmental process. Unlike traditional data analysis, the network approach can reveal topology structures of environmental systems and extract nonlinear non-stationary hidden links over a wide range of spatial/temporal scales. In this chapter, we will focus on neural networks, complex networks, downscaling analysis, and streaming data on networks.

A neural network is a massively parallel distributed processor that works much like human brains. Neurons in a neural network are designed as nonlinear information-processing units, and the interactions between neurons are mediated by synapses. Neural networks can recognize hidden patterns and correlations in raw environmental data through various Deep Learning algorithms.

Introduction to Finite Element Analysis Using MATLAB and Abaqus introduces and explains theory in each chapter, and provides corresponding examples. It offers introductory notes and provides matrix structural analysis for trusses, beams, and frames. The book examines the theories of stress and strain and the relationships between them. The author then covers weighted residual methods and finite element approximation and numerical integration. He presents the finite element formulation for plane stress/strain problems, introduces axisymmetric problems, and highlights the theory of plates. The text supplies step-by-step procedures for solving problems with Abaqus interactive and keyword editions. The described procedures are implemented as MATLAB codes and Abaqus files can be found on the CRC Press website.

✦ Table of Contents

1 Time series analysis 􀱩 1
1.1 Stationary time series 􀱩 1
1.2 Prediction of time series 􀱩 6
1.3 Spectral analysis 􀱩 13
1.4 Autoregressive moving average models 􀱩 19
1.5 Prediction and modeling of ARMA processes 􀱩 28
1.6 Multivariate ARMA processes 􀱩 37
1.7 State-space models 􀱩 43
Further reading 􀱩 47
2 Chaos and dynamical systems 􀱩 49
2.1 Dynamical systems 􀱩 49
2.2 Henon and logistic maps 􀱩 50
2.3 Lyapunov exponents 􀱩 54
2.4 Fractal dimension 􀱩 56
2.5 Prediction 􀱩 60
2.6 Delay embedding vectors 􀱩 61
2.7 Singular spectrum analysis 􀱩 62
2.8 Recurrence networks 􀱩 63
Further reading 􀱩 66
3 Approximation 􀱩 68
3.1 Deterministic and stochastic approximations 􀱩 68
3.2 Dimensionality reduction 􀱩 77
3.3 Polynomial approximation 􀱩 82
3.4 Spline and rational approximations 􀱩 88
3.5 Wavelet approximation 􀱩 93
3.6 Greedy algorithms 􀱩 105
Further reading 􀱩 108
4 Interpolation 􀱩 110
4.1 Curve fitting 􀱩 110
4.2 Lagrange interpolation 􀱩 114
4.3 Hermite interpolation 􀱩 119
4.4 Spline interpolation 􀱩 121
4.5 Trigonometric interpolation 􀱩 125
X 􀱪 Contents
4.6 Planar interpolation 􀱩 127
Further reading 􀱩 129
5 Patterns 􀱩 132
5.1 Linear and nonlinear regressions 􀱩 132
5.2 High-dimensional regression 􀱩 136
5.3 Tree-ring-based climate reconstructions 􀱩 139
5.4 Covariance analysis 􀱩 141
5.5 Discriminant analysis 􀱩 143
5.6 Cluster analysis 􀱩 148
5.7 Principal component analysis 􀱩 150
5.8 Canonical correlation analysis 􀱩 153
5.9 Factor analysis 􀱩 154
Further reading 􀱩 158
6 Estimates 􀱩 160
6.1 Numerical integration 􀱩 160
6.2 Numerical differentiation 􀱩 164
6.3 Iterative methods 􀱩 168
6.4 Difference methods 􀱩 176
6.5 Finite element methods 􀱩 181
6.6 Wavelet methods 􀱩 190
Further reading 􀱩 199
7 Optimization 􀱩 200
7.1 Unconstrained optimization 􀱩 200
7.2 The variational method 􀱩 208
7.3 The simplex method 􀱩 215
7.4 Fermat rules 􀱩 239
7.5 Karush–Kuhn–Tucker optimality conditions 􀱩 243
7.6 Primal-dual pairs of optimization 􀱩 252
7.7 Case studies 􀱩 259
Further reading 􀱩 260
8 Data envelopment analysis 􀱩 262
8.1 Charnes–Cooper–Rhodes DEA models 􀱩 262
8.2 Banker–Charnes–Cooper DEA models 􀱩 272
8.3 One-stage and two-stage methods 􀱩 274
8.4 Advanced DEA models 􀱩 276
8.5 Software and case studies 􀱩 284
Further reading 􀱩 285
Contents 􀱪 XI
9 Risk assessments 􀱩 287
9.1 Decision rules under uncertainty 􀱩 287
9.2 Decision trees 􀱩 291
9.3 Fractile and triangular methods 􀱩 294
9.4 The ε-constraint method 􀱩 303
9.5 The uncertainty sensitivity index method 􀱩 308
9.6 The partitioned multiobjective risk method 􀱩 313
9.7 The multiobjective multistage impact analysis method 􀱩 316
9.8 Multiobjective risk impact analysis method 􀱩 317
9.9 The Leslie model 􀱩 327
9.10 Leontief’s and inoperability input-output models 􀱩 331
Further reading 􀱩 334
10 Life cycle assessments 􀱩 336
10.1 Classic life cycle assessment 􀱩 336
10.2 Exergetic life cycle assessment 􀱩 339
10.3 Ecologically-based life cycle assessment 􀱩 340
10.4 Case studies 􀱩 342
Further reading 􀱩 343
11 Networks 􀱩 345
11.1 Neural networks 􀱩 345
11.2 Complex networks 􀱩 352
11.3 Downscaling analysis 􀱩 373
11.4 Streaming data on networks 􀱩 376
Further reading 􀱩 383
Index 􀱩 385