Problem of uniqueness of non-linear joint parameter identification by force-state mapping without knowing the joint model

The technique of Force-State Mapping is an important method to identify the parameters of non-linear joints. There are two approaches with the concept of Force-State Mapping, i.e., the time domain and frequency domain approaches. The advantages of the frequency domain approach compared to time domain approach are (1) the number of data points for identification can be drastically reduced; (2) it is possible to select arbitrarily the data in frequency domain for identification. In this work, an example is given to show that the above conclusion (i.e., the advantages of the frequency domain approach) is false. The result identified by the frequency domain approach is data and model dependent. One obtains different parameters when different data or model are used for identification. The reason for the non-uniqueness of the solution is that the joint force can't be determined completely by a few discrete data in the frequency domain provided that the mathematical model of the joint is not exactly known in advance.