## 5 Comparison with Newmark Method  
After validating the approach using both numerical and experimental tests we now want to evaluate the approach performance relative to a standard inverse method. We choose Newmark method which is often considered to be an industrial standard method that is used to evaluate the dynamic loads offline. For the comparison purpose we consider a simply supported beam with \(l=1\) m length and \(w=0.05\) m\(\times d=0.01\) m\({}^{2}\) cross section and the material properties: elasticity modulus \(E=2.1\times 10^{11}\) Pa, [PERSON]'s ratio \(\
u=0.3\) and density \(\rho=7800\) Kg/m\({}^{3}\). The beam is meshed using 10 uniform 8-noded hexahedron elements. The applied excitation is \(F(t)=20\sin(80\pi t)\) which is located at the bottom node between elements 3 and 4 while the beam response is measured at node A all of which are indicated in Figure 15. The remaining parameters are kept unchanged from previous tests. The computations were run on Windows PC with an Intel Core(TM)i7 3.6 GHz CPU and 32 GB of RAM. It should be noted that a similar example is also published in [50]. Figure 14: Parameter setting of load identification (**top**), initial stage of harmonic frequency excitation online identification (**middle**) and stable stage of harmonic frequency excitation online identification (**bottom**). For the comparisons we again consider the input data without any noise. We then add a Gaussian noise with zero-mean and signal-to-noise ratio of 5%. We consider a third case where a 5% deviation is added to all the modal parameters and a fourth case where both the noise and the deviation are considered together. The contaminated data will help to compare the stability of the proposed algorithm compared to Newmark method. Figure 16a-d show the results of the proposed algorithm plotted against the exact dynamic load as well as those obtained with Newmark method. The PREM and ACM errors for all these cases are listed in Table 4.  
The results show that both methods can recover the dynamic load with good accuracy when using clean data. Furthermore, the proposed algorithm has an improved accuracy compared to Newmark method. This is true for the global error PREM as well as the error in the peak value ACM. However, the proposed algorithm was able to evaluate each time step within 0.4 ms compared to 8 ms with Newmark. This is equivalent to a 95% reduction in the CPU time with the proposed algorithm. Moreover, since the considered time step is 1 ms it is possible to evaluate each time step in real time as soon as the input data is measured whereas the CPU time with Newmark method is eight times longer than the time step. The results in Figure 16b shows that the accuracy of Newmark method is significantly affected by adding the Gaussian noise where the results become meaningless as can be seen in both PREM and ACM errors. However, the proposed method still produces meaningful results and despite the relatively high PREM error, the peak value is still measured with good accuracy as reflected by the ACM error. The Newmark method seems to be less sensitive when using inaccurate modal properties, but the proposed method remains to be more accurate. Again when considering a combination of polluted data with inaccurate modal properties the proposed method still produce meaningful results which is reflected in the errors as well as Figure 16d while Newmark method again fail to produce useful results. This results suggest that the proposed algorithm is more precise and more stable against noise data when compared with Newmark method. This improved performance is achieved with a major reduction in the CPU.