# Review of Flexible Piezoresistive Strain Sensors in Civil Structural Health Monitoring
## 4 Optimization of Sensor Performance
### Improvement of Linearity  
The linearity directly reflects the sensing stability of a strain sensor, which is evaluated by the coefficient of determination (R\({}^{2}\)) of the linear regression between the electrical signal and the applied strain. A larger R\({}^{2}\) indicates a stronger linear behavior of the sensor [115], while nonlinear behaviors are more common in practice [116; 117]. In fact, the linearity relies on the degree of conductivity of the sensor. In other words, good linearity comes from high filler content, while low filler content contributes to nonlinearity [118]. This is because the dominant conductive mechanism changes gradually from the contact effect to the tunneling effect and then to the percolation effect as the filler content decreases.  
The resistance change induced by the contact effect is the dominant mechanism at the initial strain stage, leading to a linear response [119]. As for a filler content close to percolation threshold, there are not enough conductive particles to form reversible conductive paths so conductivity is mainly achieved by the tunneling effect, resulting in a nonlinear strain response under stretching [120; 121]. For instance, a strain sensor based on an Ecoflex/CNT/Ecoflex sandwich-like structure was produced with a high-dense network. The strain sensor possessed marvelous stretchability of over 500% and high linearity (R\({}^{2}\) > 0.95). However, the corresponding GF is low because of the stableconductive network formed by the high-dense filler. Other reasons for the excellent linearity of this sensor are the strong binding between the CNTs and Ecoflex substrates [80].  
In addition, the piezoresistive linearity is also influenced by the substrate property. [PERSON] et al. recently developed a highly sensitive strain sensor with graphene-woven fabrics (GWFs) on a PDMS substrate. By tuning the Young's modulus of the PDMS substrate from hundreds of kPa to a few MPa, the R\({}^{2}\) value was improved from 0.91 to 0.98 [122]. Note that some studies achieved high sensitivity and linearity simultaneously by integrating hybrid sensing materials on polymer composites [123]. [PERSON] et al. reported that an rGO/MWCNT nanocomposite film on a flexible substrate exhibited a GF of 8.5 with a high R\({}^{2}\) of 0.98. Lately, [PERSON] et al. developed a crack-assisted strain sensor with high sensitivity, high stretchability (GF > 4.2 \(\times\) 10\({}^{4}\) at 150% strain) and high linearity (R\({}^{2}\) = 0.98 within 15% strain, and R\({}^{2}\) = 0.96 from 22% to 150% strain), which were ascribed to the dense and well-controlled network cracks [124].  
In summary, the piezoresistive linearity is relevant to the change in the dominant conductivity mechanism corresponding to specific strain domains [125; 126], so that high dense, stable and robust networks will lead to a higher linearity [127]. On the other hand, the incompatibility of high sensitivity, high stretchability and satisfactory linearity was still a great challenge in developing high-performance strain sensors [42; 118].