## 1 Introduction  
The stator of a three-phase induction machine is a three-phase winding, where the rotor does not require a DC magnetic field circuit during operation; consequently, rotor currents are generated by the relative motion between the stator and rotor magnetic fields. From the interaction between stator and rotor magnetic fields, induction torque is generated in the motor [1]. Since the architecture is simple and easy to operate, induction motors have become the most commonly used AC motor. With the advancement of technology and the improvement of demand, precision control is the direction of inevitable efforts. For induction motors, their identities will not be provided solely by power, but will be promoted to the center of control. The control method and system design of the induction machine both require the equivalent model [2], which can be divided into two kinds: steady state and dynamic. The acquisition of parameters is divided into off-line estimation and on-line estimation [3]. A typical case of parameter estimation in off-line estimation is the IEEE standard 112 test, which uses the stator DC test, blocked rotor test, and no-load test to obtain the relevant parameters of the equivalent circuit [4]. In the blocked rotor test, the separation of the stator reactance and the rotor reactance is generally based on empirical rules. The no-load test emphasizes the measurement of the rotation loss. Its estimated value is sufficient for a steady-state analysis to provide approximate parameters [5]. In the differential evolution method, a broad range of each parameter was considered, and the convergence of the algorithm was satisfactory, attesting to the robustness of the method [6]. The method fits the steady-state experimental data to the stator current locus for various slip frequencies in the stator flux linkage reference-frame [7], and can better able estimate the core loss conductance. A method based on Artificial Neural Networks (ANN) and Adaptive Neuro-Fuzzy Inference Systems (ANFIS) has also been proposed [8]. This method calculates the equivalent circuit parameters using the data from the manufacturer including torque, active and reactive power, starting current, maximum torque, full load speed, and efficiency. The use of variable frequency tests for the computation of the equivalent electrical circuit parameters has also been proposed [9]. The sparse grid optimization algorithm is achieved by matching the response of the machine's mathematical model with the recorded stator current and voltage signals. This approach is noninvasive as it uses external measurements, resulting in reduced system complexity and cost [10]. An estimation method is carried out by recording the stator terminal voltage during natural braking and subsequent offline curve fitting. The algorithm allows for an accurate reconstruction of the mechanical time constant as well as loading torque speed dependency [11]. Under normal circumstances, online estimations must include equipment and controllers. When the device is connected to the controller, there must be a set of procedures to adjust its internal parameters [12; 13; 14]. In the presence of load, single-phase signals are often used for adjustment such as DC or AC signals. The DC signal can be used to adjust and determine the resistance, while the rest of the parameters must be determined by the response of the control excitation frequency [15]. In addition, some scholars have considered the magnetization curve to estimate the parameters under rated operation [16]. Constructing different operating points under different test conditions and using pulse-width modulation technology to control the excitation can also produce satisfactory results [17]. Going further, the genetic algorithm has been applied to induction motor efficiency estimation by the DC test, voltages, currents, input power, and speed measurements [18].