## 3 Advancements and Alternatives to Modal-Based Damage Identification
### Advancements to Environmental & Operational Challenges
#### 3.1.2 Pattern Recognition Methods
In the case of non-linear environmental effects, a Non-Linear Principle Component Analysis (NLPCA) may be employed, of which there are numerous variations. [PERSON] and [PERSON] [111] implemented a NLPCA method based upon the use of an Auto-Associative Neural Network (AANN), originally developed by [PERSON] [112], which uses a five-layer mapping-network whose output pattern is identical to its input pattern. The five layers consist of an input layer of measured variables, a sigmoid nodal mapping layer that projects the inputs onto the following feature-space bottleneck layer of linear transfer nodes which act as the nonlinear principle components, followed by a second sigmoid de-mapping layer that finally projects the non-linear principle components back into their original form. Once trained, the AANN is validated with undamaged data, resulting in Gaussian residual errors which can be used to determine a damage threshold for subsequent unknown input measurements. The authors tested the method on a synthetic bridge model considering nonlinear environmental effects (temperature gradient and frozen supports) and modal identified stiffness's as inputs. They found that the method was capable of detecting and quantifying introduced damage, without the need to measure environmental factors. Another method of NLPCA is Kernel Principle Component Analysis (KPCA), which incorporates a kernel function that non-linearly maps the measured variables into a higher-dimensional linear space where normal PCA can be conducted. The kernel function describes the distribution of the data using Gaussian or extreme value distribution parameters. The successful application of KPCA was carried out by [PERSON] et al. [113], who used a Gaussian kernel on modal parameters obtained from a progressive damage test conducted on the Champangshieh Bridge in Luxembourg under varying environmental and soil effects. [PERSON] et al. [114] implemented KPCA on recorded hanger tensions from the in-service Yeongjong Grand Bridge in Seoul, using a Gaussian kernel to characterise the nonlinear relationship between the hanger tensions and the unmeasured environmental and operational conditions, prior to using extreme value statistics for successful abnormality identification. In a comparative study of PCA-based algorithms for damage detection under nonlinear conditions,Santos et al. [115; 116] concluded that KPCA-based algorithms produced fewer false-positives, without significantly increasing false-negative detections when compared to standard PCA and NLPCA. The specification of two parameters is necessary for KPCA; the first is the kernel width, which represents the standard deviation of the kernel, while the second is the number of principle components extracted. These parameters have a profound effect on the performance, as the number of principal components is correlated to the number of environmental and operational parameters and the overall variance of the data. Recently, [PERSON] et al. [117] proposed a methodology of automatically selecting these two parameters through first employing Shannon's information entropy to maximize the matrix of mapped output correlations, as per [PERSON] et al. [118], to attain an accurate kernel width value, before selecting the number of principle components that represent almost all of the environmental and operational variability. Additional instances of neural network-based algorithms being successfully applied to bridges under variable environmental conditions include [PERSON] et al. 's [119] use of NN's to assess modal parameters under varying wind and temperature effects. They concluded that natural frequencies and damping ratios are dramatically affected by wind and temperature, while mode-shape sensitivity was insignificant. [PERSON] et al. [120] analysed a composite steel girder bridge (Meriden Bridge) to determine the frequency/temperature relationship and to attempt to detect damage under severe temperature fluctuations and operational conditions.