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<?php
/*
EXAMPLE ARRAY:-
array(
[field_ft_channel_id] => value of field
[field_ft_status] => value of field
[field_ft_author_id] => value of field
[field_id_14] => value of field
[field_id_15] => value of field
[field_id_16] => value of field|value of field
)
Using array_filter_key 
*/
$array = array_filter_key($array, function($key) {
    return strpos($key, 'field_id_') === 0;
});

/*
Procedural approach:
*/
$only_field_id = array();
foreach ($array as $key => $value) {
    if (strpos($key, 'field_id_') === 0) {
        $only_field_id[$key] = $value;
    }
}
/*
Procedural approach using objects:
*/
$i = new ArrayIterator($array);
$only_field_id = array();
while ($i->valid()) {
    if (strpos($key, 'field_id_') === 0) {
        $only_field_id[$i->key()] = $i->current();
    }
    $i->next();
}