You can specify the argument post_type
for the function get_posts()
(see all available arguments here). So this line
$posts = get_posts( array( 'numberposts' => -1, 'post_status' => 'any' ) );
will become this line
$posts = get_posts( array( 'numberposts' => -1, 'post_status' => 'any', 'post_type' => 'portfolio' ) );