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Liability Related to the Sale of Future Proceeds from Disposition of Subsidiary (Details) - Schedule of activity within the liability account - USD ($) | 9 Months Ended | 12 Months Ended
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Sep. 30, 2022 | Dec. 31, 2021
Schedule of Activity within the Liability Account [Abstract] |  |
Liabilities related to sale of future proceeds from disposition of subsidiaries - beginning balance | $ 59,000 | $ 322,000
Non-Cash other income recognized | (94,000) | (360,000)
Non-Cash interest expense recognized | 35,000 | 97,000
Liabilities related to sale of future proceeds from disposition of subsidiary - ending balance |  | 59,000
Less: unamortized transaction costs |  | (3,000)
Liability related to sale of future proceeds from disposition of subsidiary, net |  | $ 56,000

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- Definition Liabilities related to sale of future proceeds from disposition of subsidiaries &#8211; beginning balance. + References No definition available. + Details
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Namespace Prefix: | airi_
Data Type: | xbrli:monetaryItemType
Balance Type: | debit
Period Type: | instant

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- Definition Liability related to sale of future proceeds from disposition of subsidiary, net. + References No definition available. + Details
Name: | airi_LiabilityRelatedToSaleOfFutureProceedsFromDispositionOfSubsidiaryNet
Namespace Prefix: | airi_
Data Type: | xbrli:monetaryItemType
Balance Type: | debit
Period Type: | duration

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- Definition The amount of non-cash interest expense recognized. + References No definition available. + Details
Name: | airi_NonCashInterestExpenseRecognized1
Namespace Prefix: | airi_
Data Type: | xbrli:monetaryItemType
Balance Type: | debit
Period Type: | duration

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- References No definition available. + Details
Name: | airi_ScheduleOfActivityWithinTheLiabilityAccountAbstract
Namespace Prefix: | airi_
Data Type: | xbrli:stringItemType
Balance Type: | na
Period Type: | duration

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- Definition Amount of income (expense) included in net income that results in no cash inflow (outflow), classified as other. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 230 -SubTopic 10 -Section 45 -Paragraph 28 -URI https://asc.fasb.org/extlink&oid=126954810&loc=d3e3602-108585 + Details
Name: | us-gaap_OtherNoncashIncomeExpense
Namespace Prefix: | us-gaap_
Data Type: | xbrli:monetaryItemType
Balance Type: | credit
Period Type: | duration

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- Definition The remaining balance of debt issuance expenses that were capitalized and are being amortized against income over the lives of the respective bond issues. This does not include the amounts capitalized as part of the cost of the utility plant or asset. + References No definition available. + Details
Name: | us-gaap_UnamortizedDebtIssuanceExpense
Namespace Prefix: | us-gaap_
Data Type: | xbrli:monetaryItemType
Balance Type: | debit
Period Type: | instant