Javascript 浏览器关闭不会触发safari上的visibilityChange

我试图在用户关闭浏览器时保存一些统计信息，下面是代码

    if (typeof document.hidden !== 'undefined') { // Opera 12.10 and Firefox 18 and later support
      hidden = 'hidden';
      visibilityChange = 'visibilitychange';
    } else if (typeof document.mozHidden !== 'undefined') {
      hidden = 'mozHidden';
      visibilityChange = 'mozvisibilitychange';
    } else if (typeof document.msHidden !== "undefined") {
      hidden = 'msHidden';
      visibilityChange = 'msvisibilitychange';
    } else if (typeof document.webkitHidden !== 'undefined') {
      hidden = 'webkitHidden';
      visibilityChange = 'webkitvisibilitychange';
    } else {
      console.log('in else condition');
    }

if (typeof document.addEventListener === 'undefined' || hidden === undefined) {
      console.log("App requires a browser, such as Google Chrome or Firefox, that supports the Page Visibility API.");
    } else {
      document.addEventListener(visibilityChange, handleVisibilityChange, false);
    }

 function handleVisibilityChange() {
// Send a ajax call with **async: false**
}

上面的代码在mozilla firefox、google chrome中运行良好，但在safari中不起作用。我正在Mac Os上测试，safari版本是

12.1.1版（14607.2.6.1.1）

请问这是否是safari中的预期行为，以及作为解决方法可以做些什么

谢谢