## 1 Introduction  
Aluminum-magnesium alloys, which are classified as non-heat treatable and strain hardening alloy series, are extensively used in aeronautics and astronautics industries due to their great corrosion resistance, excellent fatigue properties, and fracture toughness, in addition to the general characteristics of aluminum alloys [1]. Welding fabrication is one of the key manufacturing methods for aluminum alloy parts [2]. In general, the variable polarity gas tungsten arc welding (VP-GTAW) process is popularly employed in the welding of thin aluminum alloy plates, in which the surface oxide film can be effectively cleaned by cathode atomization in the negative polarity stage and the base metal is principally melted in positive polarity stage [3].  
The strengthening mechanism of non-heat treatable Al-Mg alloys, typical 5 xxx series, is mainly the result of the existence of alloying elements such as magnesium and silicon that play an important role in precipitation strengthening and solid solution strengthening. Al-Mg 5 xxx series contain more than 3.0% magnesium, while the vaporization of alloying elements will occur during welding fabrication. This vaporization loss may reduce the mechanical properties of welded joints by affecting the chemical compositions of molten pool [4; 5; 6]. In order to enhance the weld quality of Al-Mg alloys, metallurgical advantages of welds produced by high-frequency pulsed and magnetic arc oscillation methods are frequently investigated, including stirring effect on molten pool, refinement of grains, reduction of distortion, and control of segregation [7; 8; 9]. A novel hybrid ultrasonic frequency pulsed VP-GTAW (HPVP-GTAW) technique has been developed in which ultrasonic frequency pulsed current is accurately superimposed in the positive polarity stage during VP-GTAW process. This process has been employed in aluminum alloy welding, and series experimental results have proven that ultrasonic frequency pulsed current is beneficial to the elimination of the weld porosity [10], the reduction of the width of HAZ [11], the increase of the weld penetration [12], the refinement of the microstructure in weld zone [13; 14; 15], and the improvement of the mechanical properties of welded joints [16; 17; 18]. However, research work on the optimization of process parameters with HPVP-GTAW has not been done before.  
The purpose of the present study was to optimize the HPVP-GTAW process parameters for enhancing the mechanical properties of 5 xxx aluminum alloy welded joints. Orthogonal design, a multi-factor and multi-level experimental method, was employed in this study. Using this method, some representative points were selected to design the experiments for the optimization of indicators, thereby reducing the number of experiments [19; 20]. Regression analysis method was also employed by regarding tensile strength, yield strength, percent elongation, and ratio reduction in area as indicators, and regression equations were obtained using the least square estimation. The optimum parameters of HPVP-GTAW process for AA 5456 aluminum alloy were obtained by analyzing the response surfaces and contour plots based on the regression equations.