Page 82 - 2025年第56卷第6期

An inverse optimization-based parameter estimation model and solution method for
neighboring rival’ hydropower station
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WANG Xiangzhen ，LI Yapeng ，CHENG Chuntian ，LI Gang ，CUI Changyue 1，2

（1. Institute of Hydropower & Hydroinformatics，Dalian University of Technology，Dalian 116024，China；

2. Dalian Research Center of Clean Energy Efficient Utilization & Electricity Market，Dalian 116024，China）

Abstract：Cascade hydropower stations have a highly coupled hydro connection，where the discharge from upstream

stations directly affects the feasibility of power generation and bidding plans for downstream stations，especially when
the upstream and downstream stations belong to different entities. Upstream stations make generation decisions based

on their own interests，which brings high uncertainty to downstream stations. To address this issue，this paper studies
a local hydropower cascade consisting of three stations. Based on the observable historical behavior data of the

upstream stations，an inverse optimization model is proposed to estimate the operational parameters and historical

data sequences，with the feasible domain of the undecided parameters determined by engineering experience. This
model is a bilevel optimization model，where the upper-level model determines the main operational parameters of

the objective station，and the lower-level model uses the parameters provided by the upper-level model to simulate
the self-interested scheduling process of the objective station. The allocation ratio of natural runoff within the basin is
also integrated into the parameters to be inferred. To solve the model with highly non-convex and multi-variable math⁃

ematical characteristics，a variable-dimensional search method based on particle swarm optimization is proposed.
Numerical examples demonstrate that the proposed inverse estimating model and variable-dimensional search method

can accurately estimate the operational parameters and historical series data of upstream neighboring stations，with
an estimation error within 2%. The proposed solving method consistently maintains strong search capabilities during

the search process，showing significant improvement over the original algorithm. Simulation experiments and statisti⁃
cal analysis further validate the reliability of the proposed model and solution algorithm.

Keywords：electricity market；cascade hydropower；inverse model；bilevel optimization；micro particle swarm opti⁃

mization
（责任编辑：尹 婧 韩 昆）
（上接第 758 页）
Study on response characteristics of asphalt concrete core wall in dam based on
bimodulus dynamic constitutive model
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LI Chuang ，SONG Zhiqiang ，WANG Fei ，LIU Yunhe ，WANG Zongkai ，NING Zhiyuan

（1. State Key Laboratory of Water Engineering Ecology and Environment in Arid Area，Xi’an University of Technology，Xi’an 710048，

China；2. Key Laboratory of Fluid and Power Machinery，Ministry of Education，Xihua University，Chengdu 610039，China）

Abstract：An appropriate dynamic constitutive model serves as a crucial foundation for evaluating the seismic perfor⁃
mance of the impervious core of asphalt concrete core dams. The results of uniaxial dynamic tension and compression
tests indicate that under low-temperature dynamic loads，hydraulic asphalt concrete exhibits a significant increase in

both tensile and compressive moduli，with a notable difference between them. Based on the Ambartsumyan bilinear

static constitutive model in the principal stress space，this paper takes into account the differences in tensile and com⁃

pressive Poisson’s ratios. The equivalent strain rate is calculated according to the principal stress state，thereby

exploring the coupling relationship among the determination of modulus，the judgment of tensile-compressive state，

and the calculation of equivalent strain rate. An incremental iterative decoupling numerical analysis algorithm is
developed，and a dynamic bi-modulus constitutive model for hydraulic asphalt concrete is established. The calcu⁃

lated tensile and compressive stress-strain curves based on the constitutive model are in good agreement with the

experimental results. Using the established dynamic bi-modulus constitutive model，a study on the response charac⁃
teristics of the core of an actual asphalt concrete core dam is conducted. Under seismic loads，the dynamic bi-

modulus effect of the core is evident. Compared with the dynamic bi-modulus model，the maximum dynamic compres⁃

sive stress of the mono-modulus model is approximately 71.4% lower. The relative difference in peak acceleration at
different positions can reach up to 25.78%. Ignoring the dynamic bi-modulus effect of asphalt concrete will lead to an
increase in the axial and vertical tensile strains of the core by 45.8% and 27.1%，respectively，resulting in an under⁃

estimation of the core's seismic capacity.

Keywords：bi-modulus dynamic constitutive model；hydraulic asphalt concrete；equivalent strain rate；core wall；

seismic response
（责任编辑：韩 昆）
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