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Graphical abstract Highlights • Structures of industrial sectors have significant impacts on energy intensity. • The energy intensity may be affected by uncertainties in industrial activities. • The randomness of energy intensity may lead to unexpected violation events. • Copula-based violation risk analysis can support decision-making in energy-intensity mitigation. Abstract An integrated approach was developed through incorporating a copula-based violation risk analysis into a programming model for optimizing industrial structures of urban clusters in uncertain conditions. Also, this approach can be used to support decision making about promoting advanced manufacturing sectors (AMSs) and mitigating industrial energy intensity. The advantages and the improvements of this approach lie in (a) reflecting the relationships between energy consumption and economic benefits in industrial sectors, and (b) incorporating the violation risk of the targets in energy-intensity mitigation into an optimizing model. A case study was conducted to illustrate the application of this approach in the Pearl River Delta of China, a highly urbanized area that includes the cities of Guangzhou, Shenzhen, Zhuhai, Dongguan, Huizhou, Zhaoqing, Foshan, and Jiangmen. The results indicated that under the desired industrial structures, violation risk of energy-intensity mitigation in the urban cluster of the Pearl River Delta would be indistinctive in the single-city perspective. Also, except Dongguan, Jiangmen and Zhaoqing, the cities of the urban cluster would achieve the goal for developing AMSs, based on the Industrial Plans for the 13th Five Year. [ABSTRACT FROM AUTHOR]