Any aggrieved person who believes the alleged violation of this article to be factually or legally contrary to this article may appeal the notice of violation to the board of adjustment and appeals in the manner provided in section 106-96 of this Code or may request that a variance be granted. An appeal and a request for variance may be filed in the alternative, but must be filed with the preventive inspection office of the public works department within 30 days of the date of the action appealed from. The board of adjustment and appeals may authorize upon appeal such variance from the terms of this article, subject to terms and conditions fixed by the board, as will not adversely affect the public health where, owing to exceptional and extraordinary circumstances, literal enforcement of the applicable provisions will result in unnecessary hardship. The burden of proof is upon the applicant to show by clear and convincing evidence that: