Optimizing capex/opex tradeoffs in built-asset engineering

Most often applied to manufactured product development, design exploration and optimization also hold potential to improve—some would say, bring long-overdue transformation to—the engineering of constructed assets: commercial and residential buildings, discrete manufacturing facilities, process and power plants, offshore platforms. While some EPC firms serving process/power and offshore markets have made substantial progress with these tools and methods, the A/E industry still has far to go in tapping their considerable potential to improve building design and manufacturing facility engineering. With the mounting economic, environmental and public-policy pressures to deliver higher-performing built assets, we expect to see DOE, MDO, Pareto optimization and robustness/reliability optimization increasingly utilized by firms engaged in architecture, engineering, construction and asset operation.

To assess the technology’s potential to benefit the AEC industry, a team led by members of CIFE—the Center for Integrated Facility Engineering at Stanford University—conducted a case study of multidisciplinary optimization of a classroom building for structural and energy performance: Flager F, Welle B, Bansal P, Soremekun G, Haymaker J (2009), Multidisciplinary process integration and design optimization of a classroom building, Journal of Information Technology in Construction (ITcon), Vol. 14, pg. 595-612, http://www.itcon.org/2009/38.

CIFE_1Design variables studied
Source: CIFE

Using Phoenix Integration’s ModelCenter, the case study evaluated a single-room classroom building, with windows on two opposite facades and a steel frame structure. The classroom design was evaluated for structural integrity, energy consumption and daylighting, as well as for initial capital cost and lifecycle operating costs. San Diego, CA was chosen as the building’s location for purposes of determining weather conditions, building regulations and energy costs.

The objectives of the study were to:

  • Minimize capital cost of the building’s steel frame, and
  • Minimize lifecycle costs for the building’s operation.

The design constraints were:

  • Structural safety—All members of the steel frame had to meet building code requirements for strength.
  • Daylighting performance—Maximum annual average lighting power multiplier of 0.6.
  • Space—Floor area fixed at 960 square feet; single-story height fixed at 10 feet.

Structural design optimization

The researchers’ preliminary investigation of the design space indicated that it was highly nonlinear, meaning small changes in variable values sometimes resulted in large changes in performance. This observation, combined with the optimization formulation being composed of only discrete variables, led them to choose a genetic algorithm to perform the structural steel optimization study. Genetic algorithms utilize processes analogous to natural selection to stochastically search for the best designs. Since they do not require objective or constraint gradient information, genetic algorithms are able to search discontinuous and “noisy” design spaces effectively. Compared with gradient-based optimization algorithms, the researchers concluded genetic optimizers were much more likely to find globally optimal designs for this problem.

The optimization problem was configured in ModelCenter’s Darwin genetic algorithm-based optimization tool. The size of the design space for a section optimization study consisted of approximately 29,575 possible designs. To optimize for structural geometry, a section optimization was conducted for each geometric configuration. Four different building lengths were studied: 24ft, 32ft, 40ft and 48ft. The following genetic algorithm parameters were used for the optimization run: Population Size = 25; Probability of Crossover = 100%; Probability of Mutation = 5%; Convergence Criteria: Fixed number of iterations = 250.

Results—The researchers’ objective in the structural optimization process was to minimize the cost of the steel frame while satisfying structural safety criteria for strength design. The genetic algorithm converged in approximately 300 iterations (1% of the total possible designs). A single iteration took approximately 10 seconds running on a desktop PC with a 3.00GHz processor and 8GB of memory.

The scatter plot below shows the results of the section optimization for beams in the structure. Each design candidate (consisting of a unique set of steel section sizes) is represented as a single point. The best performing designs (i.e., cheapest designs that satisfy the constraints) are dark blue. Grey points represent infeasible designs (i.e., those that do not satisfy the structural strength criteria). The two different swaths of design points shown in the plot correspond to the two different depths of beam section that were considered in the optimization (W12x and W14x). From the graph, one can quickly see the most efficient section sizes for the given problem as well as the tradeoff between different section sizes and depths.

CIFE_2Beam section optimization results
Source: CIFE

The parallel coordinates plot below provides an alternative view of the design space. The ranges of values for each variable are represented as a vertical axis (increasing in value from the bottom of the axis to the top). Each colored line represents a different design. As in the scatter plot, the darker blue lines represent the best designs. The point where each line intersects a vertical axis represents the value of the corresponding design variable for a particular design. Visualizing results in this fashion allows the designer to quickly identify the range of variable values that often result in the best design configurations. For example, one can see that the best designs all have a small range of beam section sizes in the two depths considered (as shown in the scatter plot). The best (blue) designs also pass through the entire range of column sections, indicating that the choice for column size from the available alternatives has less influence on design performance.

CIFE_3Impact of structural design variables on building steel cost
Source: CIFE

The parallel coordinates plot also shows that designs having a larger building length perform better. This is what might be expected based on structural engineering principles, given that roof beams are simply supported and governed by gravity loading. As the building length increases, the loading (w) increases, but the beam span (S) is reduced due to the floor area constraint defined at the outset. Therefore, as expected, the maximum bending moment decreases as the building gets longer, allowing for lighter beam sections and a cheaper overall design.

Energy design optimization

A design of experiments was conducted to evaluate performance trends over the entire spectrum of the design space. The DOE tool in ModelCenter was used to gather information about the analysis model’s behavior by running it for a number of different input variable combinations. N-dimensional parametric studies can be performed by specifying the number of samples for each of the input variables, or users can choose from a variety of predefined experimental designs including Full Factorial, Central Composite, Latin Hypercube or a customized experiment. In this case, a customized factorial was used involving the evaluation of 1881 different designs.

The researchers chose to compare the results of the DOE with the results of the optimization to evaluate differences in the two methods in terms of performance of the “best” design and the required simulation time. A gradient-based algorithm was selected to perform the optimization study because the optimization formulation comprised a single objective and continuous design variables. The algorithm chosen was called Design Explorer, developed by Boeing to solve complex problems characterized by long-running models, noisy search spaces and multiple optima. It intelligently uses non-physics-based mathematical models to reduce the number of required model executions. It is a global search algorithm, so is not likely to get stuck in local optima.

The design variables were building length, window-to-wall ratio, and orientation. The performance constraint was the annual average lighting power multiplier. The single objective function was set to minimize total lifecycle operating costs.

Results—The researchers explored the data generated by the DOE study including surface charts to understand general trends and glyph charts to study data point spreads. Tradeoffs between daylighting performance and energy performance were evaluated by varying window size, building length, and orientation. Larger windows generally result in improved daylight in the space, a reduction in artificial lighting (assuming photosensors and dimmable ballasts for the lighting), and a consequent reduction in ventilation and air-conditioning energy consumption due to the reduced heat load from the lighting energy. However, the larger windows also result in larger solar heat gains to the space and conductive losses through the fenestration, which increase the load on the HVAC system. In addition, changes to the relative total window to wall area of the building changes the relative envelope conductive heat gains/losses.

CIFE_4Glyph chart of building window and wall area vs. lifecycle operating cost
Source: CIFE

The glyph chart above shows that the designs with the lowest total lifecycle energy costs are those with the highest total wall area and the lowest total window area. Each point represents a design alternative, with blue representing the best and red the worst performing designs. Intuition would suggest that total energy consumption would be minimized when both window area and wall area are minimized; however, the chart shows that due to the geometric constraints, a design that minimizes total window area cannot result in a total wall area in the lower range of that parameter. This is an example of how data visualization capabilities in ModelCenter can allow a designer to interpret what may otherwise may be a complex and non-transparent solution space, in this case why architectural constraints prevent energy consumption from reaching the lowest possible value for the given floor area.

CIFE_5DOE results vs. optimization results. Both plots show building orientation and length vs. lifecycle operating cost
Source: CIFE

The figure above compares the results of the DOE with the optimization. The correlation between the optimum designs using DOE and the optimizer was extremely high, with the optimizer identifying the best performing design with almost the exact same design characteristics as the best design identified in the DOE. The daylighting performance constraint applied in the optimization resulted in little variation in optimum designs, since the vast majority of the designs had annual average lighting power multipliers less than 0.6 due to the shallow range of building depths relative to the range of window areas present in the design space. The number of simulations required to achieve the optimum design was reduced from 1881 to 93 (95%).

Multidisciplinary optimization

The multidisciplinary geometric design and analysis inherited the characteristics and parameters of the structural and energy analyses. The fact that the optimization formulation was composed of both continuous and discrete variables and multiple objectives led the researchers to choose Darwin to perform the multidisciplinary optimization study. For multi-objective problems, Darwin will generate Pareto tradeoff curves, with the points on the curve all being optimal in the sense that each represents a design point at which it would be impossible to improve one of the objectives without degrading the other(s). The objective functions, constraints and design variables used for the combined optimization were the ones identified in the first figure above, “Design variables studied.” Building orientation was varied from 0 degrees to 180 degrees (in 10-degree increments), the building length varied from 4 meters to 14 meters (in 1m increments), and window-to-wall ratio from 0.1 to 0.9 (in 0.1 increments). For the structural analysis, there were 65 types of girders, 7 types of columns and 65 types of beams. The design space had a population of approximately 55 x 106 possible designs. The following genetic algorithm parameters were used for the optimization run: Population Size = 25; Probability of Crossover = 100%; Probability of Mutation = 5%; Convergence Criteria: Fixed number of iterations = 250.

Results—The optimization run required 5600 iterations (0.01% of the total number of possible designs). This took approximately 34 hours on a desktop PC with a 3.00GHz processor and 8GB of memory. The tradeoff between structural costs and energy (operating) costs is shown below. The designs marked with a black “+” are Pareto optimal. One can see that the best designs from the perspective of operating cost have a relatively high capital cost and vice versa. The “optimal” design depends on the client’s preference.

CIFE_6Pareto front showing tradeoff between minimizing structural first costs and lifecycle energy costs
Source: CIFE

Only by analyzing and visualizing a large number of design alternatives is it possible to accurately characterize these tradeoffs. For example, the figure below illustrates how building length impacts the first costs and lifecycle costs of the classroom. The cost of the structure decreases as the length of the building increases because as the length of the building increases, the beam span is reduced, resulting in a more efficient (and cheaper) structural frame. From the perspective of operating costs, however, the building becomes less efficient as the building length increases. This is due to several factors, including greater surface area of building skin which results in greater conductive losses, and a larger wall area for windows to meet daylighting requirements, which results in increased solar gains and cooling requirements. This is a prime example of how designers can use design exploration and optimization to better understand performance tradeoffs, allowing them to make better informed decisions.

CIFE_7When structural costs (left) and energy costs (right) are plotted against building length, the Pareto-optimal designs show opposite performance trends
Source: CIFE

Download the full case study.

Topology optimization with its seductive biomorphic shapes is finding a vogue in some architectural engineering firms today. We hope to see forward-thinking practitioners leverage this interest to bring into wider use the less obviously sexy, but equally if not more impactful, tools and methods investigated by CIFE here. Case studies as we uncover them.